tf 

O 

En 


p 


O 


«     MH 

O 


w 
W 


D 


STRUCTURAL,    ENGINEERING 


BOOK    TWO 


CONCRETE 


EDWARD    GODFREY 

STRUCTURAL,    ENGINEER 

FOR 

ROBERT  W.  HUNT  <fc  CO. 

CHICAGO        PITTSBUEG        NEW  YOBK        LONDON 


PRICE,  $2.50 


FTJBIJSHED    BY    THE    AUTHOR 

PITTSBURG,   PA. 


^YRIGHT    1908 
OF  V1  BY 

KlQWABD  GODFREY 


£5> 


Introduction. 


This  book  is  written  to  point  the  way  to  sound  engineer- 
ing in  concrete  by  enunciating  the  principles  thereof  and 
by  laying  bare  the  falsity  of  much  that  passes  for  good  en- 
gineering in  this  comparatively  new  branch  of  construction. 
The  aim  is  to  teach,  not  by  example  or  model  or  system, 
but  by  laying  stress  on  the  principles  that  should  govern  in 
all  design.  One  of  the  evils  of  following  systems  or  models 
is  that  the  adherent  to  a  system  is  apt  to  use  it  where  it 
is  not  appropriate  and  to  hold  to  it,  without  alteration  to  suit 
the  case,  for  fear  that  alteration — improvement — would  be 
interpreted  as  confession  of  imperfection  in  the  system. 
Principles  are,  or  should  be,  of  general  application. 

There  are  four  general  divisions  to  the  book,  as  follows : 

(1)  The  first    part  consists  of  information    relative  to 
the  materials  used  in  making  concrete  and  reinforced  con- 
crete. 

(2)  The  second  part   (pages  182  to  255  incl.),  consists 
of  articles  by  the  author  which  were  published  in  Engineer- 
ing News  (New  York)  in  1906,  together  with  letters  criti- 
cising the  same,   written  by   different   engineers,   with   the 
author's  replies  to  these.     There  are  three  of  these  articles. 
The  one  on  Beams  and  Slabs  was  published  in  Engineer- 
ing News,  March  15,  1906;  the  one  on  Columns  and  Foot- 
ings was  published    July   12,   1906;   the  one   on    Retaining 
Walls  was  published  Oct.  18,  1906.     The  letters  to  the  edi- 
tor and  the  author's  replies  appeared  in  various  issues  in 
1906. 

(3)  The  third  part  (pages  258  to  413  incl.),  consists  of 
articles  by  the  author    which  were  published  in    Concrete 
Engineering  (Cleveland,  O.),  in  1907,  together  with  letters 
from  engineers  and  the  author's  replies.     There  are  eight 
of  these  articles,  and  they  appeared  serially,  beginning  with 
the  issue  of  Concrete  Engineering,  Jan.  i,  1907,  and  being 
distributed  through  the  larger  number  of  the  issues  of  that 
year.     One  article    (Domes,  etc.),  will  probably  appear  in 
the  March,  1908,  issue. 


(4)  The  last  part  of  the  book  consists  of  cuts  showing 
piers,  small  arches,  culverts,  etc.,  as  illustrating  current 
practice.  These  are  taken,  with  the  consent  of  the  pub- 
lishers, from  Engineering  News,  Engineering  Record,  Rail- 
road Gazette,  and  Street  Railway  Journal,  to  whom  the 
author  hereby  makes  grateful  acknowledgment. 

There  is  some  repetition  in  the  book  in  the  matter  of  the 
derivation  of  formulas  for  beams  and  columns,  because  of 
the  fact  that  two  of  the  articles  in  Concrete  Engineering  are 
on  the  same  subject  as  articles  in  Engineering  News.  The 
repetition  could  not  conveniently  be  avoided  in  this  com- 
pilation. 

Because  some  parts  of  the  book  are  elementary  in  char- 
acter does  not  signify  that  it  is  written  for  the  tyro.  There 
have  been  enough  examples  of  flagrant  blunders  in  public 
utterances  and  in  design  on  the  part  of  seasoned  designers 
and  eminent  engineers  to  justify  emphasis  on  ground  prin- 
ciples that  these  utterances  and  designs  violate. 

No  attempt  has  been  made  to  carry  thiough  the  book  a 
uniform  nomenclature.  Values  needed  in  any  equation  will 
be  found  close  to  it  in  the  reading  matter.  The  author  has 
found  attempted  standard  nomenclature  extremely  annoy- 
ing. A  practical  engineer  has  not  the  time,  when  he  wishes 
to  make  use  of  a  formula,  to  read  an  entire  book  in  order 
to  make  sure  of  the  meaning  of  values  in  the  formulas,  and 
he  is  only  wasting  time  when  he  must  refer  back  to  other 
chapters  for  their  meaning.  It  is  one  of  the  greatest  faults 
of  books  of  reference,  and  text  books  that  must  often  be 
used  for  reference,  that  formulas  are  set  down  with  a  view 
of  their  correctness,  solely,  the  convenience  of  the  user  in 
applying  them  being  ignored. 

Attention  is  called  to  "Some  Theses"  in  the  section  which 
follows.  In  the  author's  opinion  so  many  of  what  ought 
to  be  well-known  principles  of  mechanics  are  flagrantly  vio- 
lated in  much  current  design,  that  the  "investigations"  and 
causes  assigned  when  failures  occur  resemble  the  quibbling 
at  a  murder  trial  to  determine  whether  the  poison  adminis- 
tered to  a  sick  man,  with  "design,"  was  the  direct  cause  of 
death  or  the  disease  from  "which  he  suffered.  Studied  dis- 
regard of  the  greater  menaces  and  magnifying  of  the  lesser 
is  not  peculiar  to  investigations  of  concrete  failures,  how- 
ever. Volumes  have  been  published  in  the  few  months 
since  the  Quebec  Bridge  disaster  on  lattice  bars  and  com- 
pression members.  Some  engineers  hold  that  a  left  hand 
bottom  chord  member,  that  had  been  observed  to  be  bowed, 

2 

21451ft 


was  the  initial  point  of  failure.  Others  say  that  it  was  the 
corresponding  right  hand  chord  member,  which  was  never 
under  suspicion,  as  this  alone  would  account  for  the  fact 
that  the  top  chord  of  the  bridge  was  thrown  to  the  right 
a  progressive  amount  (10  feet  or  so  at  the  pier  and  50  feet 
out  where  the  traveler  was  located).  Still  others  would 
have  both  members  give  way  at  once,  to  account  for  the 
failure  of  the  bridge  to  lie  down  on  the  crippled  side.  The 
calculated  unit  stress  in  these  chords  at  the  time  of  failure 
is  said  to  have  been  12  ooo  Ibs.  A  quiescent  lead  of  this 
intensity  would  not,  by  anything  known  to  engineers  at  the 
present  time,  cause  these  members  to  fail.  Fourteen 
months  before  this  disaster  the  author  tried  in  vain  (by 
a  letter  to  an  engineering  journal,  which  they  declined  to 
publish)  to  utter  a  public  warning,  pointing  out  the  men- 
ace of  erecting  this  bridge  with  an  immense  traveler  lack- 
ing sway  bracing,  or  braced,  if  at  all,  with  wire  ropes, 
which  would  stretch  excessive  amounts.  This  traveler,  at 
the  time  of  failure,  held  about  500  tons  of  steel  more  than 
200  feet  in  the  air,  and  no  sway  bracing,  visible  in  any  pho- 
tographs, was  used  between  the  two  bents.  Beside  the 
roadway  the  vertical  posts  of  the  trusses  had  light  lattice 
in  planes  normal  to  the  truss,  which  would  offer  but  slight 
resistance  to  swaying,  if  the  traveler  should  lean  against 
the  top  chord  of  the  truss.  In  the  course  of  tying  up  for 
the  night  (the  wreck  happened  close  to  quitting  time) 
it  would  be  a  very  natural  sequence  of  events,  that  the 
workmen  should  take  a  block  from  the  left  side  of  the 
traveler  and  attach  it  to  the  truss  at  the  right  side,  intend- 
ing to  make  X-bracing  thus,  and  that  the  tightening  up  of 
the  line  should  start  the  top-heavy  traveler  to  moving  to 
the  right.  The  truss  would  be  inadequate  «.o  stop  it,  and 
with  just  a  little  motion  of  the  top  chord  the  vertical  posts 
of  the  truss  would  crush,  doubling  up  on  themselves.  The 
same  side  force  would  bend  in  S-shape  the  two  bottom 
chord  members  in  the  anchor  arm  which  were  located  at 
the  bottom  ends  and  the  junction  of  the  first  heavy  diag- 
onal and  first  heavy  post  of  the  anchor  arm,  causing  them 
to  fail  at  once,  which  they  undoubtedly  did,  and  alike,  as 
they  also  did.  This  hypothesis,  which  accounts  for  every 
feature  of  the  wreck  so  far  made  public,  was  ignored  for 
the  untenable  one,  from  all  present  engineering  knowledge, 
that  two  compression  members,  on  opposite  sides  of  a 
structure,  under  about  one  half  of  their  ultimate  strength 
or  less,  quietly  gave  way  simultaneously.  The  prediction 
is  here  ventured  that  when  this  bridge  is  re-erected,  the 
traveler  will  be  braced. 


A  Survey  of  the  Field  of  Concrete 
Design  and  Construction,  in  which 
will  be  Found  some  Theses. 

If  the  author  were  to  write  a  history  of  reinforced  con- 
crete, he  would  be  inclined  to  take  his  cue  from  the  writ- 
ers of  school  histories  for  juvenile  instruction  and  make  it 
a  record  of  battles  and  mortalities.  His  own  recollection 
of  school  histories  is  that  they  are  not  much  more  than  a 
list  of  wars  and  their  battles.  It  is  hard  to  conceive  what 
moral  or  intellectual  benefit  a  child  receives  from  loading 
his  memory  with  names  and  dates  of  the  battles  and  their 
casualities  that  exhibit  the  workings  of  the  passions  of 
men.  In  the  matter  of  a  new  form  of  construction  battles 
are  inevitable.  The  passions  of  men  exhibit  themselves 
here  as  elsewhere ;  but  the  battles  are  with  men  who  control 
older  forms  of  construction,  and  little  can  be  learned  or 
gained  by  recording  them.  There  are  casualties  from  an- 
other cause,  however,  the  record  of  which  would  be  in- 
structive. Reference  is  made  to  disasters  that  have  resulted 
from  errors  in  design  or  construction.  A  detailed  record 
of  these,  with  a  correct  statement  of  the  fault,  would  be 
of  great  value.  In  many  cases,  however,  if  the  truth  were 
written,  it  would  be  a  simple  statement  of  dangerous  con- 
ditions and  of  results  that  a  study  of  these  conditions  would 
lead  one  to  anticipate. 

Accidents,  of  course,  have  played  some  part  as  the 
cause  of  failures,  carelessness  and  ignorance  have  played 
a  larger  part.  Among  the  causes  assigned  to  failures  in 
reinforced  concrete  the  one  most  heard  is  "green  concrete." 
This  serves  the  purpose  to  the  builder  that  "heart  failure" 
serves  to  the  physician.  It  is  easier  to  blame  the  failure 
on  some  ignorant  or  dead  workman  who  pulled  out  the 
props  too  soon,  than  to  get  down  to  the  root  of  things 
and  discover  some  vitally  weak  part  of  the  design,  that, 
even  allowing  months  for  the  concrete  to  harden  would 
have  a  factor  of  safety  of  but  a  little  over  one. 

•4 


Another  thing  that  is  set  down  as  the  cause  of  many 
failures  is  poor  concrete.  There  is  no  doubt  that  failures 
have  resulted  both  from  the  removal  of  forms  before  the 
concrete  has  hardened  and  from  criminal  use  of  poor  con- 
crete. More  often  there  can  be  found  faults  enough  in  de- 
sign to  cast  suspicion  back  to  one  who  ought  to  be  posses- 
sed of  more  intelligence  than  the  workmen  who  are  em- 
ployed to  carry  out  the  design. 

The  importance  of  good  materials  and  their  proper 
manipulation  cannot  be  too  strongly  emphasized,  unless  that 
emphasis  obscures  other  conditions  just  as  vital  to  the 
safety  of  the  structure. 

Many  of  the  faults  in  design  very  often  met  with  are 
pointed  out  elsewhere  in  this  book;  some  of  the  most  glar- 
ing will  be  mentioned  here  at  the  risk  of  reiteration. 

When  a  column  is  made  of  such  light  section  that  in 
wood  (which  is  both  stronger  in  compression  and  immense- 
ly tougher  than  concrete)  it  would  appear  too  slender;  and 
when  that  column  is  made  of  plain  concrete  in  which  there 
are  some  longitudinal  rods ;  and  when  it  is  true  that  such 
columns  under  a  central  load  have  been  known  to  fail  un- 
der less  compression  than  others  of  plain  concrete  devoid 
of  steel,  the  concrete  in  each  being  identical ;  failure  is  the 
most  natural  thing  to  look  for,  and  that  of  an  inclusive 
and  disastrous  kind.  In  Bulletin  No.  10  of  the  Illinois  Ex- 
periment Station,  page  14,  column  8,  a  plain  concrete  col- 
umn 9"  x  9"  by  12  ft.  long  stood  an  ultimate  crushing 
strength  of  2004  Ibs.  per  sq.  in.  Column  2,  identical  in 
size  and  having  4-%"  rods  embedded  in  the  concrete,  stood 
1577  Ibs.  per  sq.  in.  This  is  not  an  exceptional  case.  Other 
series  of  tests  have  shown  the  same  thing.  It  appears  to 
be  the  rule.  Nevertheless,  one  reading  the  literature  of  re- 
inforced concrete  would  be  led  to  conclude  that  small  lon- 
gitudinal steel  rods  embedded  in  concrete  columns  add 
largely  to  the  strength  of  the  columns.  Authority  can  be 
found  for  including  in  the  strength  of  a  column  these 
slender  rods  that  would  not  stand  alone  and  that  the  sur- 
rounding concrete  supports  in  a  very  imperfect  way. 

5 


Authority  can  also  be  found  for  including  in  a  hooped  col- 
umn, apart  from  the  compressive  strength  of  the  concrete, 
the  strength  of  an  imaginary  column  of  steel,  that  is  some 
function  of  a  coil  or  set  of  hoops,  which  could  have  no 
strength  whatever  as  a  column  except  through  the  medium 
of  the  concrete,  already  given  a  value  for  its  compressive 
strength.  This  assumed  column  of  steel  is  purely  imagin- 
ary. When  phantom  columns  are  relied  upon  to  carry  ma- 
terial loads,  failure  should  not  cause  any  comment.  It  is 
just  as  rational  to  make  some  of  the  links  of  a  chain  strong- 
er than  the  others  and  then  expect  the  strength  of  the 
chain  to  be  greater,  as  it  is  to  call  the  strength  of  a  hooped 
column  the  sum  of  the  compressive  strength  of  an  imagin- 
ary steel  column,  some  function  of  the  binding  hoops  or 
spiral,  and  of  the  concrete  column.  The  latter  is  the  only 
real  column.  All  of  the  compression  must  go  through  it, 
and,  while  the  compressive  strength  of  the  concrete  is 
greater  in  flat  discs  between  hoops  that  increased  compres- 
sive strength  is  dependent  upon  the  flatness  of  the  discs 
and  is  not  dependent  upon  the  section  of  the  reinforcement, 
as  the  formula  would  make  it  appear. 

Much  misapprehension  exists  as  to  the  action  of  concrete 
in  compression.  In  tension  a  bundle  of  independent  fibres 
will  carry  a  heavy  stress.  In  compression  a  bundle  of  in- 
dependent shafts  of  slender  proportions  would  be  of  little 
use  to  carry  a  load.  A  material  that  is  weak  in  tension  can- 
not be  very  strong  in  compression  in  long  members  be- 
cause of  the  tendency  of  the  material  to  spread  laterally  and 
the  need  of  tenacity  to  prevent  this  spread.  Flat  discs  are 
very  much  stronger  than  cubes  and  cubes  are  stronger  and 
more  reliable  than  shafts  a  few  diameters  in  length.  Again 
shafts  carrying  loads  not  centrally  placed  are  much  weaker 
than  the  latter.  Perfectly  central  application  of  the  load  on 
a  column  is  something  scarcely  possible  outside  of  a  test- 
ing laboratory.  Concrete,  except  in  hooped  columns,  should 
not  be  called  upon  to  take  more  than  about  200  to  350  Ibs. 
per  sq.  in.  This  applies  to  columns  having  only  longitudinal 
rods.  It  also  applies  to  reinforced  concrete  chimneys  where 

6 


there  is  hooping;  for  the  hooping  in  a  chimney  does  not 
act  like  that  in  a  column ;  it  is  merely  to  tie  the  concrete 
together,  acting  like  the  horizontal  rods  in  a  wall.  It  also 
applies  to  an  arch  under  full  thrust.  In  beams  concrete  is 
confined  on  all  but  the  upper  side ;  the  extreme  fibre  stress 
in  beams  may  therefore  be  much  greater  than  in  unconfined 
compression  members.  Unit  stresses  of  500  to  600  Ibs.  per 
sq.  in.  may  be  safely  employed  in  beams. 

When  concrete  fails  in  compression,  spalls  break  off 
around  the  edge.  It  is  plainly  seen  that  in  a  flat  disc  these 
spalls  are  but  a  small  fraction  of  the  area  in  compression, 
hence  in  such  cases  as  a  thin  mortar  joint  heavy  compres- 
sive  stresses  can  be  withstood.  The  same  is  true  of  the 
discs  between  two  consecutive  rings  or  coils  in  a  hooped 
column.  In  cubes  the  spalls  bear  a  larger  relation  to  the 
total  area,  and  in  shafts  the  entire  surface  may  spall  off 
making  the  failure  one  in  shear.  The  fallacy  of  using 
compressive  unit  values,  found  by  testing  cubes,  to  deter- 
mine the  strength  of  concrete  shafts  with  or  without  rein- 
forcement of  longitudinal  rods,  is  therefore  apparent. 

Shear  in  steel  rods  embedded  in  concrete  at  10,000  Ibs- 
or  12,000  Ibs.  per  sq.  in.  is  one  of  the  most  blatant  absurdi- 
ties to  be  met  with  in  literature  on  the  subject  of  rein- 
forced concrete  and  in  building  codes.  It  is  totally  un- 
necessary, even  in  an  all  steel  structure,  to  specify  a  shear- 
ing unit  on  pins,  for  the  reason  that,  if  the  bearing  of  the 
parts  on  the  pin  are  properly  proportioned,  and  the  bend- 
ing moment  is  not  excessive,  the  section  will  of  necessity 
be  ample  for  the  shear.  Steel  is  thirty  times  as  strong  as 
concrete  in  bearing;  hence  there  is  something  less  than 
one-thirtieth  of  a  reason  for  specifying  any  unit  shear  on 
the  steel  rods  in  concrete.  If  so-called  shear  rods  are  pro- 
portioned on  the  basis  of  10,000  Ibs.  per  sq.  in.,  they  are 
about  as  irrationally  proportioned  as  they  could  be.  Loose 
stirrups  could  not  take  hold  of  a  horizontal  rod  to  receive 
this  shear,  except  through  the  medium  of  the  concrete; 
and,  if  the  concrete  takes  the  shear,  there  is  no  reason  why 


it  should  be  imparted  to  the  steel  rods,  since  it  must  go 
back  to  the  concrete  again  at  the  upper  part  of  the  beam. 

T-beams,  with  their  narrow  stems  and  insufficient  hori- 
zontal shearing  area  in  a  plane  above  the  bottom  rods,  offer 
another  example  of  irrational  design.  The  apparent  rein- 
forcement supplied  by  vertical  or  diagonal  shear  rods  is 
enlarged  upon  elsewhere. 

As  pointed  out,  wood  is  very  much  stronger  than  con- 
crete. Wood  will  stand  an  ultimate  load  of  10,000  Ibs.  per 
sq.  in.  or  more  in  tension  and  may  safely  take  800  to  1200 
Ibs.  per  sq.  in.  in  compression.  To  make  a  reinforced  con- 
crete member  capable  of  taking  tensile  stresses  equal  to 
what  sound  wood  will  take  there  should  be  10  or  15%  of 
steel  reinforcement  in  a  member  of  the  same  size.  To 
reinforce  a  square  member  in  bending,  as  with  rods  near 
each  corner,  so  that  it  will  be  as  strong  as  sound  wood 
for  transverse  loading,  as  in  a  column  taking  swaying 
forces,  it  would  require  5  or  10%  of  steel  reinforcement. 
Reinforcements  in  such  amounts  are  prohibitive;  it  is 
evident  then  that  concrete  members  should  be  of  larger  di- 
mensions than  members  in  wood  to  perform  the  same  office. 

Reinforced  concrete  viaducts  having  bents  composed  of 
two  inclined  posts  and  a  bottom  strut,  with  the  cross 
girder  joining  the  tops  of  the  posts,  are  not  good  construc- 
tion. In  wood  such  bents  would  be  condemned  for  lack 
of  diagonal  bracing.  Even  in  material  of  the  toughness 
of  steel  such  bents  would  not  be  attempted,  unless  diago- 
nal bracing  interfered  with  the  headroom  desired;  in  this 
case  extra  stiff  columns  would  be  used.  More  failures  of 
structures  have  been  caused  by  lack  of  proper  bracing  than 
from  any  other  cause.  The  experience  in  the  concrete  en- 
gineering field  should  make  all  builders  avoid,  as  dangerous, 
construction  that  depends  for  lateral  stiffness  upon  long 
columns  and  lacks  diagonal  bracing.  In  the  light  of  ex- 
perience and  intelligent  interpretation  of  tests,  as  well  as 
rational  analysis,  the  building  of  such  construction  only 
invites  disaster. 

Reinforced  concrete  does  not  lend  itself  to  efficient  or 
8 


economic  construction  in  open  work  resembling  steel  trusses 
or  bents.  Girders  or  bents  should  be  solid  or  nearly  so. 
Circular  openings  may  be  used  rationally  to  save  weight. 

A  common  form  of  reinforced  concrete  column  footing 
consists  of  a  square  flat  block  having  rods  lying  near  the 
bottom,  spaced  uniformly,  parallel  to  the  sides.  Some  of 
these  rods  are  entirely  outside  of  the  column  or  shaft 
carrying  the  load,  that  is,  they  do  not  lie  under  it  and  would 
therefore  serve  to  intensify  the  stress  in  rods  that  do  lie 
under  the  shaft.  This  is  another  example  of  irrational  de- 
sign. 

There  are  a  number  of  rudiments  of  popular  but  errone- 
ous notions  exhibited  in  much  reinforced  concrete  design. 
One  of  these  concerns  sharp  bends  in  rods.  A  hog  chain 
or  a  king-post  or  queen-post  truss  are  common  forms  of 
supporting  otherwise  weak  beams.  A  bent  rod  is  thrown 
under  a  beam,  and  at  the  bend  a  post  is  used  to  support 
the  beam  at  one  or  two  intermediate  points.  In  reinforced 
concrete  beams  for  test  and  in  actual  construction  it  is  very 
common  to  see  rods  similarly  bent,  and  the  appearance 
is  that  of  the  trussed  beam  just  referred  to.  With  this  the 
popular  eye  would  be  satisfied,  but  when  search  is  made 
for  something  that  corresponds  to  the  post  in  the  trussed 
beam,  nothing  is  found  but  a  trifling  amount  of  concrete 
that  occurs  at  the  bend.  To  heighten  the  absurdity  the 
so-called  truss  rod  ends  at  or  near  the  support  with  no  end 
anchorage  whatever.  It  is  as  though  the  truss  rod  in  a 
trussed  wooden  or  steel  beam  were  simply  brought  up  and 
laid  under  the  end  of  the  beam  without  an  end  nut  to  take 
the  pull.  A  hook  on  the  end  of  such  a  truss  rod  would 
correspond  to  a  hook  in  a  rod  embedded  in  concrete.  Both 
are  weak  and  inefficient. 

Sharp  bends  in  heavy  rods  are  very  common;  nothing 
could  be  more  irrational. 

It  is  a  structural  fault  in  a  design  when  steel  work  is 
so  disposed  that  there  must,  be  some  slip  before  the  part  can 
take  its  full  stress.  Such  details  are: — loose  stirrups  around 
rods,  splices  in  heavy  rods  made  by  lapping  them  and 

9 


binding  them  together,  kinks  or  short  bends  in  rods,  etc. 

Another  concession  to  popular  and  erroneous  ideas  is 
in  the  use  of  arches  where  flat  slab  construction  would  be 
better.  There  used  to  be  a  bicycle  manufactured  that  had 
a  curve  in  one  of  the  parts  of  the  frame.  Advertisements 
pointed  out  this  weakening  curve  as  a  special  element  of 
strength,  because  it  bore  some  relation  to  an  arch.  Seg- 
mental  floor  arches,  lacking  abutments  and  shallow  where 
they  need  the  greatest  depth,  and  small  arches  of  high  rise, 
pressing  horizontally  against  uncertain  earth  fill,  are  ex- 
amples of  the  persistence  of  popular  ideas. 

When  a  beam  may  be  severed  from  its  supporting  col- 
umn or  girder  by  the  mere  cracking  of  a  surface  of  con^ 
crete  and  the  pulling  out  of  a  short  length  of  rod,  and  when 
this  beam  is  an  integral  part  of  the  only  system  of  bracing 
in  a  structure,  as  in  the  case  of  a  building  where  cross 
walls  are  not  used  to  take  up  sway,  it  is  reasonable  to 
expect  that  wind  or  other  lateral  force,  acting  with  the  load 
on  the  beam  will  crack  the  beam  and  pull  out  the  rod. 

If  reinforced  concrete  is  to  be  used  in  high  buildings  to 
replace  steel  cage  buildings,  good  features  of  steel  frame 
buildings  must  not  be  overlooked.  Specifications  for  steel 
work  rightly  restrict  and  forbid  reliance  upon  tension  on 
rivet  heads  to  support  vertical  loads.  But  this  very  ele- 
ment is  of  utmost  importance  in  holding  together  and  brac- 
ing such  steel  structures  as  office  buildings  and  mill  build- 
ings. Far  too  many  reinforced  concrete  structures,  lacking 
a  unifying  element  tying  the  various  parts  together,  have 
ingloriously  failed,  and  far  too  many  laborers  and  foremen 
have  been  made  to  take  blame  that  should  have  been  at- 
tributed to  ignorance  of  designers.  It  is  of  utmost  import- 
ance that  the  parts  of  a  reinforced  concrete  building  be 
tied  together.  This  should  be  done  by  use  of  continuous 
or  spliced  rods.  The  best  way  to  accomplish  this  is  to  use 
round  rods  and  to  splice  them  with  sleeve-nuts. 

Nowhere  in  engineering  is  there  more  evidence  of  a  dis- 
position to  cover  up  ignorance  with  elaborate  cloaks  o£ 
arithmetic  fabric  than  in  reinforced  concrete  design.  This 

10 


is  exhibited  in  complex  formulas  for  the  design  of  beams, 
in  the  flat  plate  theory,  in  arch  calculations,  in  column  for- 
mulas, in  calculations  for  temperature  stresses  and  gener- 
ally where  concrete  and  steel  design  is  treated.  Some  of 
these  have  already  been  referred  to.  The  most  discredit- 
able feature  about  it  all  is  that  structures  that  have  fallen 
down  have  been  shown  by  some  of  these  applications  of 
arithmetic  to  be  quite  safe. 

Another  thing  in  evidence  is  erroneous  formulas  and  mis- 
applied methods  of  calculation. 

An  illustration  of  what  elaborate  theory  accomplishes  in 
beam  design  is  seen  from  the  following  example,  taken  at 
random.  In  Bulletin  No.  14,  Engineering  Experiment  Sta- 
tion, University  of  Illinois,  page  n,  test  beam  57  shows  a 
calculated  unit  stress  in  the  steel  of  39,800  Ibs.  This  is 
worked  out  by  a  formula  with  many  terms  and  all  of  the 
commonly  made  assumptions  that  bring  in  the  relative 
moduli  of  elasticity  of  steel  and  concrete.  The  test  load 
is  11,730  Ibs.  at  third  points  on  a  12-ft.  span.  Adding  to 
the  moment  that  this  would  give  the  dead  load  moment 
due  to  the  weight  of  the  8"  x  11"  beam  there  is  found  to 
be  a  total  moment  of  300,900  in.-lb.  Taking  the  neutral 
axis  of  this  beam  at  the  middle  of  the  depth  of  the  con- 
crete, as  the  rods  are  I  in.  above  the  bottom,  the  effective 
depth  is  8I/6  inches.  The  stress  on  the  steel  is  36,800  Ibs., 
or  on  three  %-in.  rods,  40,000  per  sq.  in.  This  is  one-half 
of  one  per  cent,  more  than  the  unit  stress  found  by  the 
elaborate  formula.  The  results  are  thus  practically  ident- 
ical in  this  case  at  least. 

The  flat  plate  theory,  as  worked  out  for  such  homogene- 
ous material  as  steel  plates,  is  given  in  all  its  elaborateness, 
as  applicable  to  reinforced  concrete  slabs  supported  on  all 
sides,  by  a  number  of  writers.  In  the  theory  of  the  flat 
plate,  as  usually  treated  a  factor  enters  that  does  not  find 
a  parallel  in  the  ordinary  theory  of  flexure.  At  the  center 
of  the  plate  the  extreme  fibre  stress  at  top  and  bottom  is 
of  the  same  intensity  in  all  directions,  in  the  two  respective 
planes.  Because  of  this  fact  the  upper  layer  is  capable  of 

11 


resisting  a  greater  intensity  of  stress  than  it  would  take 
with  the  stress  in  one  direction  only  and  the  material  not 
confined  laterally.  The  fibres  in  compression  in  a  flat 
plate  are  confined  on  all  sides,  including,  to  some  extent, 
the  side  on  which  the  pressure  is  applied.  In  the  case  of 
the  fibres  in  tension  there  is  not  this  assistance  from  con- 
jugate stress.  It  is  not  clear,  therefore,  why  Poisson's  ra- 
tio should  be  applied  to  flat  plates,  since  the  tension  on  the 
free  side  would  be  the  critical  stress.  The  term  represent- 
ing fibre  stress  in  the  flat  plate  theory  as  commonly  given 
is  not  the  true  fibre  stress  but  a  fictitious  unit  stress  re- 
sulting from  the  application  of  Poisson's  ratio.  The  actual 
fibre  stress  is  almost  cut  in  half  by  this  application.  Ad- 
vocates of  the  flat  plate  formula  do  not  seem  to  have  con- 
sidered the  question  of  converting  this  fictitious  extreme 
fibre-stress  in  all  directions  into  actual  stress  in  reinforc- 
ing steel  rods  in  two  or  more  directions.  They  further 
do  not  make  it  clear  why  all  of  the  complexity  and  uncer- 
tainty of  the  flat  plate  theory  for  steel  plates  should  be  re- 
sorted to  to  solve  flat  slabs  in  reinforced  concrete,  a  mater- 
ial not  at  all  contemplated  in  such  formulas  as  Grashofs. 

Some  prominence  has  been  given  recently  to  a  solution 
of  the  flat  slab  supported  on  four  sides,  which  starts  with 
the  assertion  that  a  flat  square  slab  supported  on  all  four 
sides  fractures  along  a  diagonal.  Assuming  that  the  bend- 
ing moment  is  greatest  along  the  diagonal  of  a  rectangular 
slab  a  formula  is  derived  for  the  magnitude  of  this  bend- 
ing moment,  which  is  naturally  a  mathematical  certainty, 
just  as  the  bending  moment  along  the  diameter  of  a  cir- 
cular plate  is  a  mathematical  certainty.  But  the  variation 
of  intensity  of  this  moment  along  the  diagonal  is  entirely 
ignored,  or  rather  the  intensity  is  taken  to  be  constant. 
There  is  just  as  much  error  in  taking  this  moment  as  uni- 
form along  the  diagonal  of  a  rectangle  as  there  is  in  taking 
the  intensity  of  the  moment  along  the  diameter  of  a  flat 
circular  plate  as  uniform.  It  may  be  true  that  a  flat  slab, 
either  square  or  rectangular,  supported  on  four  sides,  will 
break  on  a  diagonal  line.  This  is  proof  of  one  thing,  name- 
12 


ly,  that  the  greatest  intensity  of  bending  moment  is  at  the 
center  of  the  slab ;  for,  as  both  diagonals  are  identically  con- 
ditioned, either  may  be  the  one  to  fail,  and  th'eir  only  com- 
mon point  is  the  center  of  the  slab.  It  is  not  conceivable 
that  the  same  intensity  of  bending  moment  extends  clear  to 
the  corner  of  the  slab.  A  crack  once  started  in  a  diagonal 
direction  would  naturally  extend  into  the  corner  and  even 
over  the  support,  merely  on  account  of  the  brittleness  of 
the  material.  This  would  be  no  evidence  of  constant  in- 
tensity of  bending  moment  along  the  fracture ;  much  less 
force  is  needed  to  continue  a  crack  once  started  than  to 
start  the  same. 

The  author  brought  out  a  formula  for  square  slabs  sup- 
ported on  four  sides  and  reinforced  in  two  directions,  in 
Concrete  Engineering,  Feb.  I,  1907.  This  formula  is  appli- 
cable to  the  materials  considered  and  rational  in  its  deri- 
vation. It  has  the  sanction  of  Professors  Maurer  and  Tur- 
neaure,  as  it  appears  in  their  book  recently  published.  , 

In  the  design  of  arches  the  elastic  theory  has  been  em- 
phasized and  very  forcibly  recommended.  This  is  a  theory 
for  the  investigation  of  an  arch  already  proportioned.  It 
could  not  be  used  to  find  the  proportions  needed.  One  way 
recommended  to  arrive  at  a  trial  proportion  for  an  arch 
is  to  take  the  dimensions  of  existing  arches  and  judge  it 
therefrom.  An  inspection  of  a  table  of  the  proportions  of 
existing  arches  reveals  the  fact  that  they  are  hopelessly  at 
variance  with  each  other.  The  elastic  theory  requires  that 
the  moment  of  inertia  of  the  arch  at  all  sections  be  known. 
The  moment  of  inertia  of  a  combination  of  concrete  and 
steel  can  be  assumed,  or  arrived  at  by  assumptions,  but  not 
definitely  known.  The  elastic  theory,  as  usually  employed, 
assumes  fixed  ends  to  the  arch.  This  is  an  extravagant 
assumption  and  one  not  warranted  by  the  conditions.  In 
small  models  it  would  be  possible  to  make  mass  enough  in 
the  abutments  to  effect  fixed  ends  in  the  arch  span.  In 
large  arches  it  requires  massive  abutments  to  resist  over- 
turning from  the  simple  thrust  alone.  If  to  this,  mass  must 
be  added  to  make  the  ends  of  the  arch  fixed,  an  unwarrant- 

13 


ed  waste  of  material  results.  The  concrete  needed  to  add 
a  few  inches  to  the  depth  of  an  arch  ring  and  thus  increase 
by  a  large  percentage  its  stiffness  would  be  insignificant  in 
results  if  added  to  the  abutments.  The  thrust,  if  the  arch 
be  considered  hinged  at  the  ends,  is  practically  the  same 
as  if  it  be  considered  fixed  ended,  so  that  the  amount  of 
mass  in  the  abutments  due  to  assumption  of  fixed  endedness 
is  simply  extra  material  that  could  be  more  economically 
employed  in  the  arch  ring. 

The  elastic  theory  has  application  to  steel  arches  for  two 
reasons,  (i)  The  moment  of  inertia  of  a  steel  arch  can  be 
definitely  calculated.  (2)  The  unstressed  arch  fits  the  abut- 
ments upon  which  it  rests,  being  very  accurately  built  there- 
for. This  theory  is  inapplicable  to  stone  or  concrete  arches 
for  the  obverse  of  these  reasons.  The  shrinkage  of  con- 
crete in  setting  precludes  any  possibility  of  determining 
exactly  what  would  correspond  to  the  moment  of  inertia 
of  a  reinforced  concrete  section,  that  is,  a  coefficient  from 
which  the  deflection  could  be  calculated.  This  same  shrink- 
age makes  it  impossible  to  build  a  concrete  arch  of  any 
kind  that  will  be  free  from  shrinkage  stresses,  and  an  arch 
in  which  there  are  unknown  initial  stresses  should  not  be 
made  the  subject  of  exact  calculation  based  on  the  ab- 
sence of  initial  stress.  Inaccuracy  in  stone  arches  has  the 
same  result  as  shrinkage  in  concrete  arches  in  that  the 
arch  is  subject  to  some  initial  stress.  In  addition  to  this 
stone  arches  cannot  take  any  tension. 

In  the  inelastic  theory  the  presumption  of  accuracy  is  not 
made,  and  there  is  not  the  false  security  which  elaborate 
calculations  tend  to  give.  It  is  more  in  keeping  with  the 
materials  of  stone  and  concrete  arches.  A  system  of  blocks 
fitted  to  each  other  along  the  lines  of  an  arch  will  carry 
certain  fixed  loads  without  tending  to  open  any  of  the 
joints,  when  these  blocks  follow  the  line  of  what  is  called 
the  equilibrium  polygon.  When  other  loads  are  brought 
on  the  arch,  as  the  live  load,  the  equilibrium  polygon  under- 
goes certain  changes  which  would  tend  to  open  joints  at 
sections  whose  location  is  moderately  well  known.  If  the 
14 


arch  blocks  be  conceived  to  be  cemented  together  into  one 
mass  and  to  be  tied  together  by  steel  rods,  the  rods  will 
take  the  tension.  Reasonable  assumptions  to  arrive  at  the 
probable  intensity  of  the  tension  are  all  that  the  materials 
and  methods  of  manufacture  in  reinforced  concrete  arches 
justify. 

The  literature  on  stone  and  concrete  arches  is  unsatisfac- 
tory being  in  large  part  excessively  theoretical  and  unprac- 
tical from  many  standpoints.  Semi-elliptical  and  basket- 
handle  arches  are  commonly  held  out  as  examples.  Such 
curves  are  unsuitable  for  ordinary  arches,  because  they 
presuppose  heavy  horizontal  pressure  of  the  fill  or  demand 
the  same  to  prevent  large  moments  at  the  sharpening  of 
the  curve.  Only  sand  or  semi-liquid  mud  can  exert  such 
pressure  (except  as  a  wedging  force,  as  back  of  a  retain- 
ing wall)  and  neither  of  these  materials  is  desirable  as  a 
fill.  If  the  arch  is  the  roof  of  a  tunnel  under  a  stream, 
the  semi-ellipse  or  semi-circle  are  consistent  curves.  There 
is  a  general  lack  of  appreciation  on  the  part  of  writers  and 
builders,  of  the  fact  that  horizontal  pressure  in  earth,  while 
it  is  a  possibility,  is  not  necessarily  exhibited.  There  are 
many  proofs  of  this,  but  they  pass  unnoticed.  Ordinary 
earth  could  be  supported  on  a  system  of  vertical  props 
capped  with  horizontal  lagging  pieces  in  approximate  arch 
shape.  Unless  earth  will  loosen  in  large  chunks,  there  is 
scarcely  anything  to  fear  from  horizontal  pressure.  This 
action  is  not  possible  in  the  fill  over  an  arch.  Horizontal 
pressure  in  such  case  is  scarcely  a  possibility.  Of  course 
horizontal  motion  against  earth  would  meet  with  more  or 
less  resistance,  but  this  is  passive  and  not  active. 

Another  phase  of  the  impracticable  nature  of  data  on 
arches  is  seen  in  the  blanket  formulas  for  depth  at  crown. 
These  often  have  no  relation  to  the  load  to  be  carried, 
whether  heavy  or  light  traffic.  Some  of  them  give  the 
depth  of  ring  in  terms  of  the  radius  of  the  curve  of  the 
intrados,  and  usually  the  rise  is  taken  from  the  point  where 
the  intrados  begins  to  curve  away  from  the  face  of  the 
abutment.  These  details  of  outline  have  no  significance  as 

15 


determining  the  stresses  but  are  only,  architectural  features. 
The  curve  of  the  intrados  may  have  only  a  remote  relation 
to  the  real  curve  of  the  arch,  which  is  the  curve  of  the  cen- 
tral line  of  the  arch  ring. 

In  another  respect  literature  on  arches  is  unsatisfactory. 
This  concerns  live  load  stresses.  In  designing  girders  and 
trusses  in  steel,  the  live  load  can  be  placed  at  the  exact  point 
where  it  will  give  the  maximum  stress  in  any  member.  To 
do  this,  using  the  elastic  theory  in  arches,  would  introduce 
frightful  arithmetic  complications.  No  systematic  attempt 
seems  to  have  been  made  heretofore  to  determine  the  posi- 
tion of  concentrated  loads  to  give  the  maximum  effect  on 
stone  and  concrete  arches. 

Further  it  has  not  been  recognized  in  treatment  of  arches 
that  there  is  a  rise  for  any  given  span  and  loading  and  fill 
which  fits  the  conditions,  that  is,  a  point  where,  if  the  rise 
is  diminished,  the  thickness  of  arch  ring  (for  thrust)  will 
be  unnecessarily  great  to  take  care  of  eccentric  loading; 
and  if  the  rise  be  increased  the  thickness  needed  (for 
thrust)  is  not  enough  to  take  care  of  unbalanced  loading. 
This  is  the  natural  economic  rise  for  any  span. 

Calculated  stresses  in  concrete  arches  due  to  tempera- 
ture changes  are  void  of  meaning.  If  a  concrete  arch  could 
be  made  apart  from  the  site  and  then  placed  bodily  in  its 
intended  position,  and  if  it  fit  exactly  that  position,  calcu- 
lated temperature  stresses  might  have  a  meaning.  It  is 
impossible  to  place  concrete  in  such  way  that  its  normal 
unstressed  shape  fits  exactly  on  the  supports.  It  is  equally 
impossible  to  determine  the  intensity  of  stresses  due  to 
shrinkage.  If  then  the  original  condition  of  .stress  cannot 
be  known,  it  is  idle  to  make  elaborate  calculations  as  to  the 
effect  of  expansion  and  contraction  due  to  change  in  tem- 
perature. In  steel  work  arches  can  be  made  to  fit  the  sup- 
ports, and  temperature  stress  calculations  have  a  meaning. 
A  liberal  factor  of  safety  is  eminently  better  to  cover  ig- 
norance than  the  most  ingenious  mathematical  fabric  ever 
devised. 

When  a  dam  fails,  elaborate  theories  are  put  forth  to  ac- 
16 


count  for  its  overturning,  when  calculations  show  that  the 
horizontal  pressure  of  the  water  is  not  sufficient  to  tip  it 
over.  Suction  on  the  down-stream  face  is  one  of  these  bug 
bears.  There  has  been  found  to  be  a  pressure  somewhat 
below  the  atmosphere  under  a  falling  sheet  of  water  where 
the  stream  contracts,  and  this  is  seized  on  to  account  for 
the  great  force  that  would  be  necessary  to  overturn  a  mass 
of  masonry.  Or  in  the  matter  of  strength  shearing  forces 
in  vertical  or  horizontal  planes  are  blamed  for  the  failure. 
In  technical  literature  on  the  subject,  so  far  as  the  author's 
somewhat  indifferent  search  has  shown,  there  is  no  mention 
of  the  uplifting  tendency  of  water  that  percolates  under  the 
dam,  supplying  nearly  or  quite  half  enough  upward  force  to 
lift  the  masonry  of  the  dam.  This  force,  in  a  gravity  dam 
designed  to  resist  both  the  uplift  and  the  lateral  force  of 
the  water,  is  42%  of  the  total  overturning  force  or  72%  of 
the  horizontal  Iforce.  A  system  of  design  that  ignores  forces 
of  such  magnitude  as  these  and  magnifies  trifles  is  not  a 
safe  system  even  for  a  temporary  structure,  to  say  nothing 
of  the  danger  in  a  permanent  structure  upon  which  hang 
so  much  life  and  property. 

A  scheme  for  reinforced  concrete  retaining  walls,  consist- 
ing of  a  curtain  wall  and  a  bottom  slab  joined  at  intervals 
by  ribs  or  counterforts,  has  been  much  used  in  recent  years. 
Two  errors  in  design  characterize  many  of  the  designs 
that  have  been  described  in  engineering  periodicals  and  in 
books.  One  of  these  concerns  reinforcement  of  the  bottom 
slab.  Complete  reinforcement,  uniformly  distributed  for 
the  full  width  of  slab,  is  used  near  both  top  and  bottom 
surfaces.  No  analysis  of  the  forces  can  show  need  of  such 
wasteful  rise  of  steel.  In  the  matter  of  reinforcing  the  rib 
or  counter-fort  the  apparent  and  expressed  method  is  to 
treat  it  as  a  beam  with  increased  tensile  stress  from  ends 
toward  middle  of  the  inclined  edge.  This  is  far  from  cor- 
rect. The  stress  in  the  reinforcing  rods  is  imparted  at  their 
ends  and  failure  to  use  positive  end  anchorages  is  a  struc- 
tural blunder. 

In  formulas  for  reinforced  concrete  chimneys  much  un- 
17 


necessary  complication  is  sometimes  introduced  by  making 
the  neutral  axis  out  of  the  center  of  the  section.  There  is 
no  good  reason,  based  on  known  facts,  for  assuming  the 
neutral  axis  anywhere  but  in  the  center  of  the  section. 

There  is  much  misapprehension  in  the  matter  of  inter- 
pretation of  tests.  Some  published  tests  are  not  worthy 
of  the  name  of  tests.  They  are  made  for  the  purpose  of 
"proving"  the  miraculous  strength  of  some  system,  and  the 
load  is  improperly  placed  or  is  placed  on  only  a  portion  of 
the  floor.  Tests  of  shear  in  concrete  are  referred  to  at 
length  elsewhere.  Some  recent  tests  were  reported  that 
purported  to  give  the  adhesion  of  steel  to  concrete.  The 
entire  resisting  moment  of  reinforced  concrete  beams  (with 
a  short  lever  arm)  was  attributed  (so  far  as  tension  was 
concerned)  to  the  reinforcing  steel  rods,  no  allowance  being 
made  for  the  tensile  strength  of  the  concrete,  a  real  though 
uncertain  quantity.  By  using  smaller  and  smaller  rods  such 
tests  could  be  made  to  "prove"  the  adhesion  of  steel  to 
concrete  any  desired  amount;  for  even  with  no  rods  what- 
ever, the  plain  concrete  would  take  a  certain  bending  mo- 
ment. In  one  very  important  respect  the  lesson  learned 
from  tests  is  a  perverted  one.  Reference  is  made  to  the 
test  of  practical  use  of  a  structure.  There  is  no  more  mis- 
leading notion  than  the  one  that  because  a  structure  stands 
and  performs  its  office  it  is  therefore  safe.  Structures  have 
collapsed  after  standing  for  decades,  and  this  under  no 
unusual  conditions.  Given  a  structure  that  has  attained  al- 
most its  full  strength,  and  suppose  that  this  structure  fails 
when  the  forms  are  removed.  What  would  be  the  factor 
of  safety  in  such  a  structure  (or  in  another  similarly  built), 
if  it  reached  a  strength  10  or  20%  greater  and  was  capable 
of  standing  up  when  the  forms  were  removed? 

As  to  the  unit  tension  allowed  on  steel,  this  is  also  elab- 
orated elsewhere.  Units  above  10,000  to  13,000  1'bs.  per  sq. 
in.  are  too  high,  though  they  are  very  generally  recom- 
mended. At  these  units  the  concrete  will  generally  retain 
its  integrity.  Not  that  steel  can  always  be  stressed  to  this 
amount  without  cracking  the  concrete,  but,  if  there  is 

18 


enough  concrete  surrounding  the  steel,  the  tensile  strength 
of  the  concrete  will  aid  the  steel  to  the  extent,  for  safe 
loads,  that  the  elongation  will  not  crack  the  concrete.  A 
design  that  contemplates  cracks  in  the  concrete  under  safe 
loads  cannot  be  classed  as  good  engineering.  The  cause 
that  will  produce  a  crack  at  one  point  may  produce  others 
at  other  points  and  thus  break  up  and  wear  out  the  struc- 
ture. 

In  the  matter  of  the  consistency  of  concrete  there  are 
still  some  users  that  insist  on  "moist  earth"  mixtures  for 
all  purposes,  even  reinforced  concrete  and  parts  that  ought 
to  be  impermeable.  Also  it  is  very  generally  recommended 
that  materials  be  heated  before  use  in  cold  weather.  A  very 
significant  letter  appears  in  Eng.  News,  Jan.  30,  1908  from 
Mr.  E.  A.  Mollan.  He  describes  some  concrete  that  was 
made  with  sand  and  stone  that  had  been  dried  out  by  the 
heat  of  the  sun.  This  concrete  had  no  cohesion  and  was 
worthless.  When,  subsequently,  the  same  materials  were 
wetted  down  concrete  made  therewith  (using  the  same 
cement  as  before)  was  of  good  quality.  Builders  who  make 
use  of  stoves  to  heat  and  dry  the  sand  and  stone  for  con- 
crete are  commended  to  a  study  of  this  case. 


19 


Cement. 

There  are  two  kinds  of  cement  in  common  use,  namely,. 
Rosendale  or  natural  cement  and  Portland  cement.  To- 
this  may  be  added,  also,  slag  cement  or  puzzolan  cement. 

Rosendale  cement  is  made  by  burning  a  limestone  con- 
taining the  carbonates  of  lime  and  magnesia  and  clay  at 
about  the  temperature  of  the  lime-kiln  or  1000  to  2000- 
degrees  F.  It  is  ground  to  a  powder  between  mill  stones 
after  burning.  The  color  is  usually  brown.  Rosendale 
cement  is  used  to  some  extent  in  foundations  for  street 
pavements  and  in  some  massive  concrete  work.  It  should 
not  be  used  in  reinforced  concrete  work  or  in  work  where 
strength  is  to  be  an  important  characteristic. 

Portland  cement  is  made  by  mixing  clay  and  limestone 
(or  other  argillaceous  and  calcareous  substances)  in  the 
proper  proportions,  and  burning  the  mixture  at  a  high, 
heat  (above  2000°  F.),  and  grinding  the  clinker  to  a  pow- 
der. The  color  is  usually  gray  or  greenish  gray.  There 
are  four  different  kinds  of  Portland  cement  manufactured 
in  the  United  States  as  distinguished  by  the  materials.- 
from  which  the  cement  is  manufactured.  These  com- 
binations are:  i.  Argillaceous  limestone,  or  cement  rock,, 
and  limestone.  2.  Marl  and  clay.  3.  Hard  limestone  and 
shale  or  clay.  4.  Slag  and  limestone. 

There  is  a  kind  of  cement  called  slag  cement,  or  puzzo- 
lan cement.  This  is  made  by  first  granulating  the  slag 
by  chilling  the  molten  slag  in  water,  then  drying  and  mix- 
ing with  slaked  lime,  then  grinding.  This  is  an  inferior  ce- 
ment and  is  only  good  in  locations  where  it  will  be  con- 
stantly wet.  The  color  of  slag  cement  is  light  lilac.  Slag 
cement  should  not  be  confused  with  true  Portland  cement 
made  from  slag  and  limestone.  The  latter  is  made  by 
burning  to  a  clinker  a  mixture  of  crushed  limestone  and 
chilled  blast  furnace  slag  and  then  grinding  this  clinker 
as  the  clinker  of  other  Portland  cement  is  ground.  A 
description  of  the  manufacture  of  this  kind  of  cement  is 
given  in  Engineering  News,  Sept.  27,  1900. 

20 


These  cements  are  all  what  are  called  hydraulic  cements, 
that  is,  they  will  set  or  become  hard  under  water.  They 
are  unlike  common  lime  in  this  respect,  as  they  do  not  re- 
quire the  presence  of  air  to  acquire  their  cementing  qual- 
ity. The  presence  of  water  is  necessary  to  the  hardening 
of  cement,  and  cement  will  harden  both  in  fresh  or  salt 
water.  Unlike  lime,  also,  the  clinker  from  which  cement 
is  manufactured  is  inert.  The  unground  lumps  are  like 
cinders,  and  they  are  therefore  useless  in  this  state.  It 
is  only  when  the  clinker  is  ground  very  fine  that  it  is  fit 
for  use  as  a  cement.  This  is  the  reason  why  fine  grinding 
is  essential  in  all  hydraulic  cement. 

An  average  analysis  of  good  Portland  cement  is  about 
as  follows:  Lime,  64%;  Silica,  21%;  Alumina,  8^%; 
Magnesia,  2^%;  Iron  Oxide,  2^/2%;  Other  ingredients, 
i%%.  A  variation  one  way  or  the  other  of  2%  or  so  in 
the  amount  of  lime  and  silica  does  not  make  much  dif- 
ference in  the  cement.  The  magnesia  should  not  exceed 
about  2  or  3%.  There  is  not  so  much  regularity  in  the 
composition  of  Rosendale  or  in  slag  cement  as  there  is 
in  Portland  cement.  There  is  generally  much  less  lime 
and  more  silica  and  magnesia  in  Rosendale  than  in  Port- 
land. 

Portland  cement  is  superior  to  Rosendale  for  every  pur- 
pose, for  a  given  volume  of  cement,  though  the  latter 
for  many  uses  meets  the  requirements  of  the  case/  Nat- 
ural or  Rosendale  cement  sets  quicker  than  Portland  ce- 
ment, though  Portland  cement  soon  overtakes  and  passes 
the  natural  cement.  The  quick-setting  property  of  natural 
cement  may  be  turned  to  advantage  in  work  that  is  to  re- 
ceive its  load  soon  after  placing.  By  using  a  larger  quan- 
tity of  natural  cement  than  would  be  needed  in  Portland 
cement  the  necessary  strength  may  be  attained  in  a  short 
period. 

Natural  and  Puzzolan  cements  will  not  stand  extreme 
changes  in  temperature  as  well  as  Portland  cement. 

When  sand  and  cement  are  mixed  and  ground  together, 
the  mixture  can  be  ground  finer  than  it  is  possible,  with 


the  same  means,  to  grind  the  cement  alone.  It  can  in 
fact  be  ground  so  fine  that  nearly  all  of  it  will  pass  through 
a  sieve  having  200  meshes  to  the  inch.  On  account  of  the 
extreme  fine  grinding,  and  possibly  also  on  account  of  the 
activity  of  the  sand  in  this  finely  divided  state,  the  cement 
is  stronger  than  the  same  amount  of  ordinary  cement 
would  be.  If  the  installation  of  a  grinding  mill  is  practi- 
cable on  a  large  piece  of  work,  where  the  cost  of  cement 
is  high,  there  may  be  a  saving  in  thus  grinding  a  mixture 
of  cement  and  sand  in  order  to  reduce  the  amount  of  ce- 
ment required.  The  grinding  of  a  mixture  of  cement  and 
sand  is  patented. 

The  weight  of  Portland  cement  is  85  to  100  Ibs.  per  cu. 
ft.,  depending  upon  whether  it  is  loose  or  compact.  A 
barrel  of  cement  is  considered,  by  some  specifications,  as 
equal  to  four  cubic  feet.  This,  at  375  Ibs.  per  standard 
barrel,  is  about  94  Ibs.  per  cu.  ft. 

The  tests  commonly  made  on  cement  are  given  else- 
where in  this  book.  A  few  notes  on  the  method  of  mak- 
ing these  tests  and  the  importance  of  the  tests  would  not 
be  out  of  place  here.  Some  additional  tests  will  also  be 
mentioned. 

To  determine  whether  or  not  a  cement  is  hydraulic  mold 
a  brick  i"xi%"x8",  and  after  the  initial  set  place  it 
under  water  upon  supports  near  the  ends,  having  the  one- 
inch  dimension  vertical.  If  the  cement  is  hydraulic  the 
brick  will  retain  its  shape,  if  not,  it  will  give  way  between 
the  supports. 

A  simple  test  for  soundness  of  cement,  or  freedom  from 
tendency  to  shrink  or  expand  during  setting,  is  to  take  a 
cylindrical  lamp  chimney  and  fill  it  for  a  certain  distance 
with  well  compacted  cement  paste,  marking  the  end  of  the 
flat  surface.  If  the  cement  shrinks,  it  will  show  by  the 
mark,  and  if  it  swells,  it  will  break  the  chimney. 

The  swelling  of  cement  during  setting  is  usually  due 
to  the  slaking  of  free  lime.  When  the  cement  is  used 
fresh  from  the  mill  it  is  apt  to  have  some  free  lime  in  it. 
Seasoning  for  several  weeks  after  grinding,  if  the  cement 

22 


is  finely  ground,  will  air  slake  this  lime  and  render  the 
cement  more  sound.  On  the  other  hand  too  long  expos- 
ure to  the  air  will  destroy  the  activity  of  the  cement  and 
may  render  it  useless.  Moist  air  is  especially  destructive 
on  the  cement.  It  should  therefore  be  stored  in  a  dry 
place.  Air  generally  affects  cement  by  causing  it  to  cake 
in  the  sacks,  and  the  hard  lumps  that  cannot  be  easily 
broken  with  the  shovel  will  be  useless  as  cement.  Good 
cement  may  be  somewhat  lumpy,  but  the  lumps  should  be 
such  that  they  can  be  easily  broken  with  the  fingers. 

The  test  for  fineness  of  cement  is  important,  because  the 
finer  a  cement  is  ground  the  stronger  that  cement  will  be. 
Not  only  is  the  activity  of  the  cement  increased  by  fine 
grinding,  but  the  fine  particles  are  necessary  to  fill  small 
voids  in  the  sand  and  thus  render  the  mortar  or  concrete 
dense. 

The  test  for  specific  gravity  is  made  to  determine  wheth- 
er or  not  the  cement  is  properly  burned  and  also  to  de- 
lect adulterants.  If  Portland  cement  is  under-burned,  its 
specific  gravity  will  be  low,  and  if  it  is  over-burned,  its 
specific  gravity  will  be  high.  Specific  gravity  tests  are  apt 
to  be  misleading,  because  of  the  fact  that  the  cement  ab- 
sorbs some  C  O  2  and  water  from  the  air  and  thus  its 
specific  gravity  is  reduced.  Cements  having  different  de- 
grees of  calcination,  if  tested  when  fresh-burned,  or  if 
heated  red  hot  before  testing,  to  drive  off  absorbed  C  O  2 
and  water,  appear,  according  to  Mr.  David  B.  Butler, 
(Eng.  Record,  Vol.  55,  p.  176)  to  have  very  close  to  the 
same  specific  gravity.  Mr.  Butler's  tests,  however,  do  not 
discredit  the  value  of  the  specific  gravity  determination  to 
detect  adulterants.  Natural  cement  or  slag  used  as  adul- 
terants will  lower  the  specific  gravity. 

The  conclusions  in  a  paper  by  Prof.  R.  K.  Meade  and  Mr. 
S.  C.  Hawk,  read  before  the  American  Society  for  Test- 
ing Materials  in  June,  1907,  drawn  from  a  series  of  tests 
made  by  them,  are  as  follows : 

"(0  That  the  specific  gravity  test  is  of  no  value  what- 
ever in  detecting  underburning,  as  underburned  cement 

23 


will  show  a  specific  gravity  much  higher  than  that  set  by 
the  standard  specifications.  Underburned  cement  is  read- 
ily and  promptly  detected  by  the  soundness  test  and  no 
others  are  needed  for  this  purpose. 

"(2)  The  value  of  the  specific  gravity  test  as  an  indi- 
cation of  adulteration  is  much  exaggerated.  While  a 
large  admixture  of  any  light  adulterant  with  the  cement 
would  be  shown  there  is  at  the  same  time  much  slag  ce- 
ment and  also  Rosendale  cement  which  could  be  mixed 
with  cement  in  large  quantities  without  lowering  the  speci- 
fic gravity  below  the  limit  of  our  standard  specifications. 

"(3)  That  low  specific  gravity  is  usually  caused  by 
seasoning  of  the  cement  or  the  clinker,  either  of  which 
improves  the  product. 

"(4)  That  the  proposition  to  ignite  the  cement  sample- 
which  falls  below  specifications  and  determine  the  speci- 
fic gravity  upon  the  ignited  portion  is  of  no  value  because 
adulterated  cements  also  have  their  specific  gravity  very 
much  raised  by  such  ignition. 

"(5)  That  the  requirements  for  specific  gravity  should 
be  omitted  from  the  standard  specifications  or  at  least 
that  the  clause  which  infers  that  low  specific  gravity  is 
caused  by  underburning  and  adulteration  should  be  omit- 
ted and  that  in  its  place  there  should  be  inserted  one  stat- 
ing that  low  specific  gravity  may,  but  does  not  necessarily 
imply  adulteration  as  it  is  in  most  cases  due  to  seasoning 
of  the  cement  or  storage  of  the  clinker  before  grinding, 
both  of  which  are  beneficial  to  the  product." 

Specific  gravity  of  cement  is  usually  determined  by  im- 
mersion in  benzine  or  turpentine. 

The  addition  of  a  small  quantity  of  unburned  granu- 
lated slag,  before  grinding,  to  cement  made  from  slag" 
is  not  considered  an  adulteration,  as  it  neutralizes  the 
effect  of  any  free  lime  that  may  be  in  the  cement. 

Cement  that  shows  excessively  high  tensile  strength  in 
short  time  tests  is  liable  to  be  adulterated  with  sulphates, 
which  hasten  the  settling  but  render  the  cement  weak  after 
a  long  time. 

24 


In  making  pats  or  bricquetts  for  test  the  paste  should 
be  mixed  thoroughly  for  five  minutes,  rubbing  the  mix- 
ture under  pressure.  Regularity  should  be  observed  in 
placing  the  mortar  in  the  molds.  Pressure  should  be 
used,  and  as  near  the  same  pressure  as  possible  for  dif- 
ferent tests.  A  difference  in  the  amount  of  tamping  or 
pressure  may  make  a  very  great  difference  in  the  strength 
of  tensile  tests. 

Soundness  of  cement  is  of  more  importance  in  rich  mix- 
tures than  in  lean  mixtures.  Cement  that  will  stand  the 
28-day  test  for  soundness,  but  fail  under  the  accelerated 
test  by  boiling  or  steaming,  may  be  satisfactory  in  ordin- 
ary concrete.  Cement  that  will  stand  both  the  accelerated 
and  the  28-day  test  is  to  be  preferred.  Cement  that  shows 
up  well  in  the  accelerated  test  is  not  necessarily  a  good 
cement.  The  presence  of  sulphates  seems  to  counteract 
the  expansive  effect  of  free  lime.  Gypsum  or  sulphate  of 
lime  is  generally  added  by  manufacturers  of  cement  to  re- 
tard the  set.  Sulphate  of  lime  to  the  extent  of  more  than 
two  per  cent,  by  weight  is  not  allowed  in  any  cement  by 
the  U.  S.  Army  engineers ;  not  more  than  one  per  cent. 
is  allowed  in  cement  to  be  used  in  sea  water. 

Cement  that  shows  up  well  in  the  tensile  test  after  seven 
days  and  then  shows  little  or  no  gain  at  28  days  is  to  be 
looked  upon  with  suspicion. 

The  tests  given  in  cement  specifications  are  to  be  made 
in  a  laboratory  equipped  for  the  purpose.  Simple  tests 
may  be  made  on  the  work,  that  will  in  some  cases  be 
sufficient  to  determine  the  general  character  of  the  ce- 
ment. Pats  and  balls  of  cement  or  mortar  can  be  made 
use  of  to  gage  the  setting  qualities  and  soundness.  By 
pressure  of  the  thumbnail  the  setting  quality  may  be 
estimated  and  by  dropping  the  hardened  specimens  a 
rough  idea  may  be  had  of  the  strength. 

Puzzolan  or  slag  cement  may  be  detected  by  taking  a 
pat  and  boiling  it  for  several  hours  and  then  breaking  it. 
The  fresh  fracture  will  be  bluish  green. 

The  following  is  quoted  from  "Professional   Papers  of 

25 


the  Corps  of  Engineers,  U.  S.  Army.  No.  28."  "Puzzolan 
cement  never  becomes  extremely  hard  like  Portland,  but 
Puzzolan  mortars  and  concretes  are  tougher  or  less  brit- 
tle than  Portland.  The  cement  is  well  adapted  for  use  in 
sea  water,  and  generally  in  all  positions  where  constantly 
exposed  to  moisture,  such  as  in  foundations  of  buildings, 
sewers  and  drains,  and  underground  works  generally,  and 
in  the  interior  of  heavy  masses  of  masonry  or  concrete. 
It  is  unlit  for  use  when  subjected  to  mechanical  wear, 
attrition  or  blows.  It  should  never  be  used  where  it  may 
be  exposed  for  long  periods  to  dry  air,  even  after  it  has 
well  set.  It  will  turn  white  and  disintegrate,  due  to  the 
oxidation  of  its  sulphides  at  the  surface  under  such  ex- 
posure. Sulphuretted  hydrogen,  which  is  often  evolved 
upon  decomposition  of  the  sulphides  in  Puzzolan  cement, 
is  injurious  to  iron  and  steel.  Such  metals,  if  used  in 
connection  with  Puzzolan  cement,  should  be  protected, 
or  an  allowance  be  made  for  deterioration  by  an  increase 
of  section." 

Cement  is  considered  by  most  authorities  to  be  a  sub- 
stance which  attains  its  hardness  by  a  process  of  crystalli- 
zation, taking  up  the  water  used  in  mixing  to  form  a  hy- 
drate of  a  crystalline  structure.  The  author  believes, 
with  Dr.  William  Michaelis  of  Germany  that  cement  does 
not  crystallize  in  hardening,  but  that  it  is  a  colloid.  The 
author  believes  that  the  nature  of  cement  is  more  nearly 
represented  by  ordinary  glue  than  by  any  crystalline  sub- 
stance, and  that  what  crystallization  takes  place  is  inci- 
dental and  not  a  necessary  accompaniment  of  the  harden- 
ing process.  Cement  clinker  is  inert :  it  does  not  slake  like 
quicklime;  it  must  be  first  ground  to  a  powder  to  have 
any  cementing  quality.  It  is  only  the  impalpable  powder 
of  this  so-called  cement  that  is  really  cement.  The  rest 
is  inert,  like  the  clinker.  Pure  neat  cement,  used  alone, 
would  not  get  very  hard  and  would  not  be  very  strong. 
Laitance,  or  the  slime  that  rises  to  the  surface  in  a  ce- 
ment mixture  in  an  excess  of  water,  is  the  nearest  thing 
to  pure  cement  that  is  usually  encountered.  So-called 

2Q 


neat  cement  is  a  mixture  of  small  particles  of  inert  clink- 
er and  a  dust  that  is  fine  enough  for  water  to  act  upon 
and  turn  into  a  colloid  or  gellatinous  substance,  which, 
when  lodged  in  between  small  grains  of  an  inert  hard  sub- 
stance, holds  these  grains  together  in  an  artificial  stone. 
The  inert  hard  substance  may  be  grains  of  sand  or  the 
coarser  grains  of  ground  cement  clinker,  too  coarse  to 
have  cementing  properties. 

The  foregoing  statements  are  radically  different  from 
the  commonly  accepted  belief  regarding  cement.  They 
therefore  call  for  some  facts  to  substantiate  them.  No 
attempt  will  be  made  to  discuss  the  chemistry  of  cement, 
except  to  cite  some  admitted  facts  that  bear  in  a  general 
way  on  its  chemical  action. 

It  is  well  known  that  fine  grinding  improves  the  strength 
•of  cement.  It  is  also  known  that  there  is  a  point  beyond 
which  fine  grinding  diminishes  the  strength  of  cement 
when  made  into  neat  briquettes  and  pulled.  It  is  also 
known  that  this  same  finely,  ground  cement,  that  is  weak- 
er in  neat  tests  than  coarser  cement,  is  stronger  in  ce- 
ment and  sand  tests  than  the  other. 

Another  fact  well  known  is  that  when  a  broken  piece 
of  china  is  to  be  mended  by  glue,  or  when  two  pieces  of 
wood  are  to  be  glued  together,  the  parts  must  be  pressed 
firmly  together  and  as  much  of  the  glue  squeezed  out  as 
possible;  and  the  strength  of  the  mended  part  is  greater 
than  that  of  the  glue  itself  by  which  it  was  mended. 

Lime  mortar,  even  before  it  has  had  time  to  be  acted 
upon  by  the  carbon  dioxide,  is  stronger  in  tension  than 
the  lime  paste. 

Melted  sulphur  is  used  sometimes  as  a  cement,  usually, 
however,  alone.  In  Engineering  News,  Vol.  51,  p.  231, 
Mr.  Alexander  Potter  describes  some  tests  on  melted  sul- 
phur as  a  cement  for  sewer  pipe,  mixed  with  sand.  He 
finds  it  to  be  an  excellent  material  for  that  purpose.  In 
his  tests  he  found  plain  sulphur  to  resist  tension  with  an 
ultimate  strength  of  about  100  Ibs.  per  sq.  in.  Sulphur  and 
sand  mixed  hot,  I  of  sulphur  to  I  of  sand  stood  650  Ibs. 

27 


per  sq.  in. ;  5  of  sulphur  to  7  of  sand  stood  670  Ibs.  per  sq. 
in. ;  2  of  sulphur  to  i  of  sand  stood  400  Ibs.  per  sq.  in. 
Mr.  Potter  found  that  fine  sand  such  as  quicksand  gives 
better  results  than  coarser  sand.  These  strengths  were 
shown  as  soon  as  the  sulphur  was  cold.  This  is  analogous 
to  the  action  of  Portland  cement.  When  very  finely 
ground,  it  has  an  overdose  of  cement  and  not  sufficient 
inert  substance  to  be  cemented  together.  When  sand 
is  added  till  a  balanced  mixture  is  formed,  the  mortar 
is  strong.  Sometimes  sand  and  cement  tests  pull  up 
stronger  than  neat  cement.  Cement  reground  with  sand 
is  made  much  finer  and  will  take  in  more  sand  to  form  a 
balanced  mixture.  The  mixture  may  be  unbalanced  by 
having  too  much  cement,  as  in  the  sulphur  tests,  where 
more  sand  added  makes  the  specimen  stronger;  or  it  may 
be  unbalanced  by  having  too  much  inert  substance  to  have 
the  interstices  filled  by  the  cement,  as  in  lean  mixtures  of 
sand  and  cement. 

That  Portland  cement  is  a  mixture  of  a  cementing  sub- 
stance (the  finest  powder)  and  an  inert  substance  may  be 
shown  by  the  following  experiment.  Take  a  little  cement 
and  mix  it  in  about  ten  times  its  volume  of  hot  water. 
Let  this  boil  for  several  hours,  adding  more  water  as  re- 
quired. At  the  end  of  this  time  stir  up  the  mixture  and 
pour  it  rapidly  into  a  tumbler.  Almost  immediately  there 
will  be  a  settlement  of  part  of  the  cement,  which  is  of  a 
dark  color.  Upon  this  there  will  settle  a  light  colored 
part  of  the  cement,  leaving  the  water  comparatively  clear. 
A  distinct  line  will  separate  the  dark  colored  and  the  light 
colored  parts.  The  upper  layer  will  be  slimy  at  first  then 
gellatinous,  and  will  finally  (in  a  week  or  two)  attain  a 
slaty  hardness.  Upon  drying  it  becomes  like  chalk  and 
has  little  cohesion.  The  lower  layer,  which  in  an  experi- 
ment by  the  author  was  about  equal  in  volume  to  the  up- 
per layer,  is  like  sand  and  has  little  cohesion.  It  can  be 
crumbled  in  the  fingers.  The  upper  layer  is  the  slime  or 
laitance  or  true  cement  that  is  liberated  in  an  excess  of 
water,  when  concrete  is  mixed.  The  fineness  of  the  grinding 

23 


will  no  doubt  gage  the  relative  amounts  of  inert  and  ac- 
tive substance  in  the  cement.  In  a  repetition  of  this  ex- 
periment the  cement  was  allowed  to  settle  in  a  glass,  and 
the  water  was  poured  off.  The  separated  cement  was  then 
mixed  together  into  a  mortar  and  allowed  to  harden. 
It  hardened  into  a  cohesive  and  hard  lump. 

By  the  use  of  cold  water  and  long  continued  agitation 
a  partial  separation  can  be  effected,  but  enough  of  the  fine 
dust  seems  to  adhere  to  the  inert  particles  to  cement  them 
together.  The  light  and  dark  colors  will  be  present  but 
they  will  not  be  so  clearly  defined. 

Some  tests  presented  in  a  paper  by  Messrs.  Henry  S. 
Spackmand  and  Robert  W.  Lesley,  read  before  the  As- 
sociation of  American  Portland  Cement  Manufacturers  at 
their  annual  convention  in  1907  (See  Eng.  Record,  Dec. 
21,  1907,  p.  691,)  prove  very  conclusively  that  a  large 
part  of  commercial  Portland  cement  is  inert  on  account 
of  not  being  fine  enough  to  have  any  activity.  Briquettes 
of  neat  cement  were  made  and  at  periods  of  from  7  days 
up  were  tested.  At  28  days  they  stood  a  tensile  test  of 
752  Ibs.  per  sq.  in.  These  broken  briquettes  were  then 
dried  and  reground.  This  material  was  used  as  cement 
and  made  into  briquettes,  which  stood,  at  28  days,  253  Ibs. 
per  sq.  in.  These  broken  briquettes  were  dried,  reground, 
and  used  again  as  cement.  The  briquettes  stood  163  Ibs. 
per  sq.  in.  at  28  days.  Tests  were  made  at  other  periods, 
and  mortar  tests  were  made  with  sand.  The  above  illus- 
trates what  the  tests  demonstrate.  In  the  words  of  the 
experimenters — "These  experiments  clearly  show  that 
even  after  cement  has  been  twice  gaged  with  water  and 
allowed  to  harden  under  water,  all  the  cementing  and  hy- 
draulic qualities  are  not  destroyed."  It  is  clear  that  the 
regrinding  of  the  briquettes  broke  up  particles  that  were 
not  fine  enough  to  be  active  at  the  first  and  second  gagings. 

The  paper  above  referred  to  describes  other  experiments 

that    further    strengthen  the    conclusion    that    the    finest 

ground   Portland    cement   is    composed    largely  of    inert 

clinker,  too  coarse  to  be  active.  Quoting  the  paper  again.— 

29 


"Portland  cement  which  had  passed  the  20O-mesh  sieve 
was  further  separated  by  elutriation  into  the  following 
parts :  (A)  Material  that  settled  out  in  30  seconds ; 
(B)  Material  that  remained  in  suspension  for  30  seconds, 
but  settled  out  in  one  minute;  (C)  Material  that  re- 
mained in  suspension  for  more  than  one  minute.  The  ce- 
ment thus  divided  into  three  portions  according  to  size 
was  treated  with  water  in  tightly  stoppered  tubes.  "A" 
was  only  slightly  acted  upon  by  water,  even  after  two 
years  contact  with  it.  "B"  was  only  acted  upon  by  water 
after  three  or  four  months,  and  only  a  portion  became 
fully  hydrated.  "C"  was  acted  upon  almost  immediately, 
swelling  up  and  forming  a  very  voluminous  jelly."  [Elu- 
triation is  shaking  up  in  dry  kerosene  and  allowing  to  set- 
tle. The  amount  of  this  cement  that  settled  in  30  seconds 
is  not  stated.  In  another  sample  45.18  per  cent,  settled  in 
this  time.] 

When  a  substance  crystallizes,  the  crystals  assume  a 
definite  volume  and  have  not  the  property  of  swelling  to 
a  larger  volume  or  of  occupying  less  space.  Further,  these 
crystals  have  the  property  of  exerting  pressure  to  reach 
that  given  volume,  as  exhibited  in  crystals  that  form  in 
the  pores  of  soft  stone  swelling  with  such  force  as  to  crack 
the  stone.  Sound  cement  will  not  swell  with  force  as 
crystallizing  substances  do.  It  is  true  that  cement  that 
hardens  under  water  will  swell  slightly,  but  the  same  ce- 
ment hardening  in  the  air  will  shrink,  proving  the  lack 
of  definite  volume  in  the  hardened  cement.  On  the  other 
hand  cement  that  is  not  confined  by  the  inert  particles 
pressing  against  it  can  be  made  to  swell  to  fill  a  space 
much  larger  than  its  original  volume.  The  minute  grains 
of  cement,  if  they  are  finely  broken  up,  have  the  property 
of  swelling  to  many  times  their  size  by  the  absorption  of 
water  and  hardening  in  water  or  in  air.  If  abundance  of 
water  be  present,  the  grains  will  swell  up  to  a  larger  size 
and  make  a  more  dense  and  a  stronger  mortar;  and,  if 
the  water  be  present  for  a  sufficient  time,  the  cement 
will  unite  with  some  of  it  and  harden  in  this  larger  vol- 

30 


time.  Upon  being  taken  out  of  the  water  after  being 
thoroughly  hardened  the  cement  does  not  then  contract 
in  drying  out,  but  the  surplus  water  dries  out  of  the  min- 
ute pores  in  some  such  way  as  a  cork  that  has  been  soaked 
in  hot  water  dries  out,  though  the  water  would  not  pass 
through  the  pores  of  the  cork  in  a  liquid  state. 

The  amount  of  water  permanently  retained  by  the  ce- 
ment in  an  ordinary  concrete  mixture  or  in  mortars  of 
about  i  :3  is  about  16  to  18  per  cent,  of  the  weight  of  the 
cement.  In  neat  cement  only  about  8  to  12  per  cent,  is  re- 
tained. This  is  further  evidence  of  the  fact  that  the  hard- 
ening of  cement  is  not  a  crystallizing  process.  Crystals 
have  a  definite  amount  of  water  in  their  composition.  It 
is  evidence  also  that  the  pure  cement  will  swell  and  ab- 
sorb water  in  proportion  to  the  space  to  be  filled  and  the 
amount  of  water  present,  as  the  voids  in  mortar  are  much 
greater  than  in  neat  cement ;  also  the  amount  of  water 
present,  even  in  mealy  concrete,  is  greater  than  needed  in 
neat  cement  mortar.  These  facts  would  further  seem  to 
vitiate  the  contention  of  those  who  say  that  only  the  bare 
amount  of  water  for  the  needs  of  the  cement  should  be 
used  in  the  mixing,  since  cement  under  varying  conditions 
will  combine  with  different  amounts  of  water. 

When  cement  is  mixed  with  a  meagre  amount  of  water, 
the  grains  do  not  have  the  conditions  present  that  promote 
free  swelling  to  fill  the  voids.  The  result  is  that  the  mor- 
tar or  concrete  is  porous,  that  is,  full  of  large  pores  that 
allow  the  passage  of  water.  It  is  an  erroneous  belief  that 
the  impermeability  of  concrete  is  promoted  by  using  a 
meagre  amount  of  water  in  mixing  and  tamping  this  con- 
crete. 

It  is  well  known  that  concrete  can  be  made  quite  good 
that  is  deposited  in  water  and  it  is  well  known  that  speci- 
mens that  are  kept  in  water  after  setting  will,  upon  hard- 
ening, be  very  much  better  and  stronger  than  like  speci- 
mens hardened  in  air.  It  is  not  clear  why  authorities, 
in  the  face  of  these  facts,  warn  against  the  use  of  plenty; 
of  water  in  the  mixing. 

31 


Dr.  William  Michaelis,  in  a  paper  read  at  the  annual 
meeting  of  the  Association  of  German  Portland  Cement 
Manufacturers  at  Berlin  in  Feb.  1907  (See  Cement  and 
Engineering  News,  Aug.  1907)  describes  a  piece  of  arti- 
ficial stone  made  of  Portland  cement  and  10  or  20  per 
cent,  of  asbestos  fiber.  The  mixture  was  stirred  a  long 
time,  as  paper  pulp  is  stirred,  and  then  pressed  to  expel 
the  surplus  water.  The  volume  of  the  stone  was  many 
times  that  of  the  volume  of  the  cement  used  in  the  mix- 
ture, showing  that  the  cement  had  swollen  by  the  absorp- 
tion of  water  to  attain  this  volume.  Dr.  Michaelis  says 
of  this  stone  that  it  is  rightly  named  eternite,  for  it  is 
practically  everlasting.  The  stone  resembles  slate.  There 
is  a  company  that  makes  this  kind  of  artificial  stone  for 
shingles.  According  to  those  who  advocate  a  mealy  mix- 
ture for  concrete  this  stone  would  be  expected  to  be  por- 
ous and  totally  unfit  for  shingles  on  account  of  the  large 
excess  of  water  used  in  making  it.  The  presence  of  the 
asbestos  fiber  and  the  long  continued  agitation  hold  the 
grains  of  cement  apart  and  allow  them  to  swell  by  the  ab- 
sorption of  water. 

Pure  cement  when  placed  in  water  will  swell  to  many 
times  its  volume  measured  as  a  dry  powder,  if  not  confined. 
In  commercial  neat  cement,  however,  the  particles  of  in- 
ert clinker  act  to  confine  the  pure  cement  and  prevent  the 
swelling.  If  there  is  plenty  of  water  in  the  mixture,  and 
the  cement  is  well  mixed  through  the  mass,  the  cement 
will  swell  to  fill  the  voids  and  will  bind  together  the  in- 
ert particles  making  a  stronger  and  better  concrete  than 
can  be  made  by  a  mealy  mixture,  even  with  pressure  ap- 
plied in  the  manufacture.  If  the  swollen  cement  dries 
out  before  it  has  hardened,  the  concrete  will  shrink.  This 
is  the  reason  why  cement  or  concrete  hardened  in  water 
will  swell,  and,  if  hardened  in  the  air,  it  will  shrink.  This 
is  the  cause  of  shrinkage  cracks  in  work  that  has  not  been 
kept  moist  during  hardening. 

Tests  for  soundness  or  constancy  of  volume  in  neat 
cement  may  be  misleading,  because  of  the  fact  that  the 

32 


best  cement,  that  is,  the  finest  ground  cement  and,  other 
things  being  equal,  that  most  suitable  for  concrete,  may 
show  the  poorest  results.  The  greater  proportion  of  very 
fine  flour  gives  the  better  cement  a  tendency  to  swell, 
whereas,  a  cement  containing  less  fine .  flour  and  more 
inert  clinker  might  show  greater  constancy  of  volume. 

Cements  that  do  not.  show  up  well  in  neat  tests  for 
constancy  of  volume  may  be  quite  sound  in  mortar  or 
concrete,  though  of  course  the  cause  of  swelling  in  a  test 
may  be  the  presence  of  free  lime  or  magnesia  and  may 
have  no  relation  to  the  fineness  of  grinding. 

lame. 

Lime,  while  it  is  not  ordinarily  used  in  making  concrete, 
is  of  importance  because  of  its  use  in  mortar  and  be- 
cause it  may  be  made  use  of  in  decreasing  the  permeabil- 
ity of  cement  concrete,  also  because  it  is  one  of  the  con- 
stituents in  the  manufacture  of  slag  cement. 

Common  lime  is  made  by  roasting  or  burning  lime- 
stone, or  carbonate  of  calcium.  The  roasting  reduces  the 
carbonate  to  oxide  of  calcium  or  quick-lime.  Quick-lime 
usually  contains  from  5  to  10  per  cent  of  impurities.  The 
impurities  retard  the  process  of  slaking,  so  that  lime  should 
be  slaked  several  days  before  it  is  used  in  mortar,  so  as 
to  be  thoroughly  slaked  when  placed  in  the  wall.  The 
swelling  of  lime  in  slaking  would  be  detrimental  to  the 
strength  of  the  wall.  Lime  may  be  slaked  and  packed  in 
barrels  for  an  indefinite  length  of  time,  or  it  may  be  kept 
in  the  mixing  boxes  covered  with  sand.  It  is  when  lime 
mortar  is  exposed  to  the  air  and  absorbs  carbon  di-oxide 
therefrom  that  it  becomes  hardened  and  that  it  acts  to 
cement  together  the  bricks  or  stone  of  a  wall.  Kept  in 
the  form  of  a  paste,  with  only  the  surface  of  the  mass 
exposed  to  the  air,  this  absorption  of  carbon  di-oxide  will 
not  take  place  to  any  great  extent.  Quick-lime,  if  ex- 
posed to  the  air,  will  absorb  not  only  moisture,  but  car- 
bon di-oxide  as  well.  Air  slaked  lime  will  make  weak 

33 


mortar  on  account  of  the  premature  absorption  of  the 
C  O  2  and  the  formation  of  what  is  commonly  known  as 
whiting.  Lime  should  therefore  be  fresh-burned. 

Neat  lime  would  be  of  little  use  as  a  cementing  mater- 
ial on  account  of  its  weakness  and  the  necessity  of  its 
being  in  thin  layers  to  enable  the  air  to  have  access  to  it. 
It  should  be  used  only  to  fill  the  voids  in  some  material 
such  as  sand  or  brick  dust. 

A  barrel  of  lime  will  make  about  eight  cubic  feet  of 
stiff  paste.  The  weight  of  a  barrel  of  lime  is  230  pounds. 
This  is  three  bushels  or  3.75  cu.  ft.. 

Lime  comes  in  lumps,  as  it  needs  no  grinding  after 
burning,  on  account  of  the  fact  that  the  action  of  the 
water  in  slaking  breaks  up  the  lumps  into  a  powder.  If 
the  lime  is  found  in  a  powder,  it  indicates  that  it  is  air 
slaked.  The  slaking  of  lime  requires  about  two  parts 
by  weight  of  water  to  one  of  lime. 

Fat  or  rich  lime  is  lime  made  from  pure  or  nearly  pure 
carbonate  of  calcium.  Dolomite  is  a  limestone  contain- 
ing magnesia.  Lime  made  therefrom  is  poor  or  meagre, 
that  is,  slow  in  slaking  and  not  fat  or  rich. 

Hydrated  lime  is  a  product  lately  come  into  extended 
use  for  the  various  purposes  for  which  slaked  lime  may 
be  used.  This  is  a  very  fine  white  powder  produced  by 
slaking  in  a  rotary  pan  quick-lime  that  has  been  broken  up 
into  small  lumps.  Sufficient  water  is  used  to  slake  the 
lime  and  still  leave  it  hot  enough  to  drive  off  the  surplus 
water,  leaving  a  dry  powder.  This  powder  is  sifted  or 
screened  to  remove  unburned  or  unslaked  lime  and  any 
coarse  particles.  The  hydrated  lime  is  sold  in  sacks. 
This  is  used  in  mortars :  in  the  manufacture  of  sand-lime 
bricks  and  of  slag  cement ;  in  hard  wall  plasters,  either 
mixed  with  Portland  cement  or  gypsum  products ;  as  an 
addition  to  Portland  cement  mortar  to  make  it  more 
easily  worked  and  to  retard  the  settling;  in  rendering  con- 
crete more  dense  and  waterproof. 

The  action  of  lime  in  the  manufacture  of  what  are  called 
sand-lime  brick  is  quite  different  from  its  action  in  or- 

34 


dinary  mortar.  Part  of  the  sand  used  in  making  sand- 
lime  brick  is  very  finely  ground,  and  thus  rendered  ac- 
tive in  some  such  way  as  the  inert  clinker  from  which 
hydraulic  cement  is  made  is  rendered  active  by  grinding. 
The  bricks  are  cured  in  steam  under  pressure  and  the 
presence  of  C  O  2,  instead  of  being  necessary,  is  undesir- 
able. The  chemical  action  is  between  the  lime  and  the 
finely  powdered  sand. 

Sand. 

Sand  is  the  term  commonly  applied  to  small  particles 
of  quartz;  it  is  also  used  to  designate  small  particles  of 
stone  such  as  crusher  dust  or  very  small  gravel.  The 
maximum  size  of  grains  admitted  under  the  term  sand 
is  sometimes  as  large  as  %  in.,  while  sometimes  finer 
sand  is  required.  Ordinarily  about  one-sixteenth  of  an 
inch  is  the  maximum  size  of  grain. 

Standard  sand,  used  in  making  mortar  tests,  is  crushed 
quartz  that  passes  a  sieve  with  20  meshes  to  the  inch  and 
is  retained  on  a  sieve  of  30  meshes  to  the  inch. 

Sand  with  angular  grains  is  called  sharp  sand.  Bank 
sand  is  usually  a  sharp  sand,  while  river  and  sea  sand 
generally  have  rounded  grains  on  account  of  the  wearing 
of  the  particles  on  each  other.  Formerly  specifications 
generally  called  for  sharp  sand.  The  sharpness  of  sand  has 
been  found  to  have  but  little  relation  to  its  value  in  ce- 
ment mortar  or  in  concrete,  and  sharp  sand  is  not  so 
often  demanded.  The  most  important  quality  in  sand  is 
the  grading  of  the  sizes  of  grains  from  coarse  to  fine. 

If  spheres  of  equal  size  and  having  radii  of  unity  be 
stacked  so  as  to  have  the  least  percentage  of  voids,  each 
may  be  considered  as  enclosed  in  a  solid  having  12  faces, 
each  of  which  is  a  rhombus  whose  long  diagonal  is  2  and 
whose  short  diagonal  is  the  square  root  of  2.  The  vol- 
ume of  the  sphere  is  74.05  per  cent,  of  that  of  the  solid. 
The  voids,  therefore,  in  a  stack  of  spheres  placed  as  com- 
pactly as  possible  would  be  nearly  26  per  cent  As  sand 

35 


is  composed  of  more  or  less  rounded  grains,  we  would 
look  for  a  percentage  of  voids  approaching  this.  How- 
ever, on  account  of  the  friction  it  is  difficult  to  compact 
sand  of  grains  sifted  to  a  uniform  size  to  a  density  show- 
ing less  than  about  44  per  cent,  of  voids.  It  is  found 
that  the  voids  in  compacted  sand  of  varying  sized  grains 
amount  to  about  30  per  cent.  The  percentage  in  ordin- 
ary sand  varies  between  30  and  45. 

In  general  sand  having  a  large  sized  maximum  grain, 
that  is,  coarse  sand,  is  a  stronger  sand  for  mortar  or  con- 
crete than  fine  sand.  Many  fine  sands  are  unfit  for  use 
in  mortar  and  concrete.  Such  sands  could  be  improved 
by  the  addition  of  a  coarse  sand,  using  a  quantity  of 
each  in  the  mixture  for  mortar  or  concrete.  By  making 
several  mixtures  and  comparing  tests  therefrom  with  a 
standard  a  satisfactory  sand  may  be  obtained,  and  fine 
sand  that  might  be  available  and  cheap  could,  by  the  pur- 
chasing of  some  coarse  sand,  be  made  use  of  to  advantage. 
If  only  fine  sand  is  available,  its  weakness  may  be  counter- 
acted by  the  use  of  a  larger  proportion  of  cement. 

Sand  containing  much  mica  is  apt  to  be  weak,  as  mica 
will  not  adhere  well  to  the  cement. 

Sand  should  not  contain  much  foreign  substance  of  a 
soft  nature,  such  as  clay  or  silt.  If  this  foreign  sub- 
stance is  in  the  shape  of  lumps,  it  is  especially  bad,  as 
these  will  make  weak  spots  in  the  concrete.  Lumps  should 
be  eliminated  by  sifting  in  preference  to  washing.  Fine 
particles  of  clay  in  sand,  found  naturally  in  the  same  and 
thoroughly  mixed  through  the  mass,  do  little  or  no  harm. 
Clay  has  been  found  by  some  experimenters  to  reduce  the 
strength  and  by  others  to  increase  it.  The  reason  for 
this  discrepency  is  no  doubt  found  in  the  difference  in 
the  nature  of  the  clay.  If  the  clay  is  added  to  the  sand, 
the  probabilities  are  that  it  will  weaken  the  mortar,  un- 
less the  clay  is  first  finely  ground.  If  the  clay  is  found 
in  the  sand  naturally,  it  will  probably  add  to  the  strength, 
because  it  is  then  more  apt  to  be  in  a  finely  ground  state. 
It  is  only  when  the  clay  is  in  the  finest  kind  of  a  powder, 


or,  if  moist,  in  a  finely  divided  state,  and  thoroughly 
mixed  through  the  mass  that  it  has  a  beneficial  effect  on 
the  mortar. 

Many  tests  have  shown  sand  containing  5  to  10  per 
cent,  or  more  of  fine  clay  to  be  stronger  in  a  mortar  than 
clean  sand.  A  little  clay  increases  the  density  of  the 
mortar.  Sand  containing  more  than  10  or  15  per  cent, 
of  clay  or  silt  should  be  used  only  after  thorough  tests 
and  not  at  all  on  such  work  as  reinforced  concrete.  The 
ultimate  effect  of  the  clay  on  the  life  of  the  concrete  is  a 
matter  of  doubt,  even  though  short  time  tests  do  show  an 
increase  of  strength  because  of  its  presence.  In  mas- 
sive concrete  the  sand  may  contain  10  to  15  per  cent,  of 
clay  and  still  be  suitable.  In  reinforced  concrete  it  should 
contain  no  more  than  5  or  10  per  cent.  In  concrete  blocks 
no  more  than  5  per  cent,  should  be  allowed.  Trie  richer 
the  mixture,  in  general,  the  greater  the  detrimental  effect 
of  foreign  substances  in  the  sand.  Clay  is  less  harmfull 
in  coarse  sand  than  in  fine  sand.  It  helps  to  fill  the 
voids  in  coarse  sand,  while  it  holds  the  particles  of  sand 
apart  in  fine  sand. 

If  sand  is  found  to  contain  an  excess  of  clay,  it  can 
be  washed  to  remove  the  clay.  Washing,  however,  be- 
sides being  expensive  is  liable  to  take  out  the  fine  grains 
of  sand,  which  are  of  great  importance,  as  these  fill  the 
small  voids  and  make  the  concrete  dense  and  strong. 
The  washing  of  sand  may  be  done  by  use  of  an  inclined 
trough  with  a  gate  at  the  low  end.  Sand  is  placed  at 
the  high  end  and  played  upon  with  a  hose.  The  clean 
sand  settles  at  the  low  end  of  the  trough,  and  the  dirty 
water  flows  over  the  gate.  Sand  should  be  tested,  washed 
and  unwashed,  to  determine  whether  washing  is  profit- 
able. 

If  sand  is  ignited,  clay  will  be  broken  up,  and  to  some 
extent  burnt,  and  thus  rendered  less  harmful  on  account 
of  being  more  durable.  This,  too,  would  be  an  expensive 
operation. 

Dirt  in  sand  is  to  be  viewed  with  suspicion.     Natural 

37 


sands  are  seldom  found  mixed  with  soil,  unless  it  be  for 
a  small  depth  on  the  top  of  the  bed.  The  dirt  may  have 
been  incorporated  into  the  sand  as  a  result  of  handling. 
At  the  site  the  sand  should  not  be  laid  in  the  dirt,  as  the 
last  of  it,  when  shoveled  up  may  contain  an  excessive 
amount  of  dirt  and  be  the  cause  of  a  weak  batch  of  con- 
crete. 

Good  clean  sand  may  be  mixed  with  sand  containing 
an  undesirable  amount  of  clay  and  the  mixture  made 
acceptable  by  this  means.  This  would  be  preferable,  in 
some  cases  to  washing  and  losing  the  fine  particles. 

The  best  material  for  good  strong  concrete  is  coarse, 
clean  sand. 

Sea  sand  contains  alkaline  salts  which  induce  efflor- 
escence. These  should  be  dissolved  out  with  fresh  water. 

Stone  dust  or  screenings  are  sometimes  found  superior 
to  sand  in  mortar  tests. 

Dry  sand  weighs  ordinarily  from  90  to  loo  Ibs.  per  cu. 
ft.  A  common  weight  assumed  for  ordinary  sand  is  2600 
Ibs.  per  cu.  yd.  Sand  having  very  large  and  very  small 
grains  may  weigh  as  much  as  117  Ibs.  per  cu.  ft.  or  more 
than  3000  Ibs.  per  cu.  yd. 

The  specific  gravity  of  quartz  is  2.65,  hence  a  solid 
block  of  one  cu.  ft.  would  weigh  165  Ibs.  The  voids  In 
quartz  sand  may  be  calculated  from  the  weight  per  cu.  ft. 
by  noting  the  per  cent,  that  it  falls  short  of  165.  Pure 
sand  weighing  100  Ibs.  per  cu.  ft.  has  close  to  40  per  cent, 
of  voids. 

Besides  its  use  as  a  constituent  of  concrete  and  mor- 
tar sand  is  used  in  casting  artificial  stone  blocks.  For 
this  purpose  the  sand  is  made  use  of  just  as  in  a  foun- 
dry. It  is  found  to  absorb  the  surplus  water  In  the  mix- 
ture, and  this  keeps  the  mold  moist. 


38 


Aggregates. 

The  term  aggregate  is  used  by  the  author  to  mean  the 
solid  inert  part  of  concrete  not  included  in  the  term 
sand,  and  not,  as  used  by  some  writers,  to  include  the 
sand.  This  is  the  rational  use  of  the  term.  There  is 
need  of  a  single  word  to  apply  to  the  third  term  in  the 
ratio  of  a  concrete  mixture,  on  account  of  the  variety  of 
substances  that  may  be  employed.  A  1 :2  14  concrete  means 
in  America  a  mixture  of  one  part,  by  volume,  of  ce- 
ment to  two  parts  of  sand  (whether  this  be  siliceous 
sand  or  rock  screenings)  to  four  parts  of  aggregate. 
This  use  of  the  term  is  very  common  and  convenient. 
Anyone  who  would  force  a  different  meaning  to  a  term 
in  common  use,  because  of  fancied  perversion  of  its  true 
meaning,  is  commended  to  the  work  of  restoring  the 
word  manufactured  to  its  true  meaning,  "hand  made." 

The  aggregates  used  in  concrete  are  usually  gravel, 
broken  stone,  and  cinders.  Besides  these  shells,  broken 
bricks,  and  slag  are  sometimes  employed. 

Gravel,  when  it  comes  in  assorted  sizes,  is  a  very  good 
material  for  concrete  from  several  standpoints.  First,  it 
is  usually  hard  and  durable  stone  that  has  withstood  at- 
trition, and  is  the  result  of  natural  selection.  Second, 
the  stones,  being  round,  will,  if  graded  in  size,  make  a 
dense  mixture,  and  the  denser  the  mixture  of  a  given 
material  the  stronger  the  concrete.  Third,  gravel  will 
resist  fire  better  than  many  other  kinds  of  stone.  The 
round,  smooth  surface  of  gravel  is  not  as  good  a  surface 
for  the  cement  to  take  hold  of,  and  for  this  reason  bro- 
ken stone  concrete  may  be  stronger,  though  it  may  not  be 
as  dense  as  gravel  concrete.  However,  the  density  of 
gravel  often  overcomes  this,  and  gravel  concrete  is  some- 
times stronger  than  stone  concrete.  Some  experimenters 
have  found  gravel  to  be  stronger  than  broken  stone  in 
concrete.  The  surface  of  gravel  concrete  cannot  be  tooled 
as  well  as  that  of  broken  stone  concrete,  Because  the 
gravel  stones  break  out  under  the  force  of  the  tool. 
39 


Crushed  gravel  is  sometimes  used  in  concrete.  This  is 
a  very  good  material,  if  the  gravel  is  a  good  clean  vari- 
ety. 

Gravel  is  apt  to  be  mixed  with  dirt,  either  in  the  form 
of  lumps  of  coal  or  of  slimy  covering  on  the  stones,  or, 
as  in  the  case  of  sand,  in  the  form  of  an  admixture  of 
clay,  mud,  or  silt.  Such  gravel  should  be  washed  or  re- 
jected. The  objection  to  the  washing  of  sand  does  not 
apply  with  the  same  force  to  gravel,  as  the  gravel  is  not 
required  to  contain  the  very  viine  particles  that  should  be 
a  constituent  of  all  good  sand. 

Broken  stone  should  be  hard  and  durable.  Concrete 
cannot  be  strong  if  made  of  weak  stone.  The  stones 
should  not  have  incipient  cracks,  so  that  they  will  crush 
under  the  rammer.  They  are  best  to  be  nearly  cubical, 
at  least  not  in  flat  flakes,  as  such  stones  will  not  pack  well. 
The  stone  should  be  uniform,  that  is ;  there  should  not 
be  just  a  few  of  the  largest  size  of  stones,  or  an  excess 
of  the  same;  also  there  should  not  be  an  excess  of  dust, 
say  not  over  15  per  cent,  of  very  small  particles.  The 
whole  pile,  as  well  as  different  deliveries  should  be  well 
mixed,  so  that  different  batches  of  concrete  will  be  as 
near  alike  as  possible.  There  should  not  be  over  one 
per  cent,  of  rotten  stone.  Unloading  of  the  stone  is  apt  to 
separate  the  large  stones  from  the  small  ones.  Dumping 
in  dirty  places  may  result  in  a  large  quantity  of  dirt 
getting  into  a  batch  of  concrete. 

The  kinds  of  stone  generally  used  are  trap,  limestone, 
and  sandstone.  Trap  is  the  best  of  these,  as  it  is  harder 
and  stronger  than  the  others  and  is  a  better  fire  resistant. 
Hard  limestone  is  good  and  durable,  except  as  to  its  abil- 
ity to  withstand  fire.  It  will  calcine  or  turn  to  lime  un- 
der heat.  Sandstone  is  not  as  strong  as  the  others. 

In  an  aggregate  such  as  gravel  and  broken  stone  used 
in  concrete  strength  and  density  are  desired.  These  are 
closely  related.  The  mixture  that  will  pack  the  closest 
will  give  the  strongest  concrete  in  a  given  quality  of 
stone.  The  voids  in  broken  stone  usually  run  from  40  to 

40 


5o  per  cent,  of  the  volume.  These  voids  must  be  filled 
up  with  mortar,  or  the  mixture  of  sand  and  cement  in 
the  concrete.  The  smaller  the  amount  of  voids  the  better 
will  be  the  concrete.  Tests  have  shown  the  unexpected 
in  the  matter  of  the  sizes  of  the  broken  stone  or  gravel, 
namely;  that  ftie  mixture  that  has  the  largest  maximum 
size  of  stones,  if  the  sizes  are  properly  graded,  will  be 
the  densest  and  strongest.  Many  specifications,  particu- 
larly earlier  ones,  read  as  though  it  were  a  serious  fault 
to  have  sizes  of  stones  too  large  to  pass  through  a  given 
sized  "ring,"  and  many  of  these  same  specifications  re- 
quire also  that  screenings  be  rejected  from  the  mixture. 
Both  of  these  requirements  are  detrimental  to  the  strength 
of  the  concrete.  A  mixture  in  which  the  medium  size  of 
stones  predominates  will  not  be  a  dense  mixture;  the 
exclusion  of  large  stones  and  very  small  ones  tends  to 
produce  this  very  condition.  It  is  well  known  that  stones 
of  large  size  have  less  surface  for  a  given  weight,  hence 
there  is  less  surface  to  cover  with  cement  in  concrete  of 
large  aggregates,  besides  less  voids  to  fill.  However, 
there  are  practical  reasons  for  limiting  the  maximum  size 
of  stones  in  most  concrete  work.  Some  of  these  are  the 
danger  of  air  spaces  forming  under  large  stones  and  of 
their  arching  and  leaving  voids  not  filled  with  mortar. 

Given  an  aggregate  having  a  certain  maximum  size 
of  stones,  the  densest  and  best  mixture  will  be  found 
when  about  one-third  of  the  weight  is  composed  of  pieces 
less  than  one-tenth  of  the  maximum  dimension,  and  one- 
third  is  composed  of  pieces  between  one-tenth  and  one- 
half  of  the  maximum,  and  one-third  is  composed  of  pieces 
more  than  one-half  of  the  maximum.  For  example,  sup- 
pose a  mixture  has  stones  that  will  measure  not  over  one- 
inch  maximum  size.  One-third  of  this  mixture  should 
pass  through  a  sieve  having  10  meshes  to  the  inch,  and 
two-thirds  of  the  total  should  pass  through  a  sieve  hav- 
ing two  meshes  to  the  inch.  There  should  be  graded 
sizes  in  all  the  aggregate,  from  the  largest  to  the  smallest 

41 


size,  to  fill  the  graded  sizes  of  voids  that  will  of  necessity 
occur. 

In  general,  in  a  concrete  mixture,  an  aggregate  having 
a  large  maximum  size  of  stones  demands  a  sand  of  large 
maximum  size  of  grains,  while  an  aggregate  having  a 
smaller  maximum  size  of  stones  should  have  a  sand  of 
small  maximum  size  of  grains.  Thus,  if  the  maximum 
size  of  stones  is  2*/&  in.,  the  maximum  size  of  sand  grains 
may  be  *A  in.,  and  if  the  maximum  size  of  stones  is  ^ 
in.,  that  of  the  grains  of  sand  may  be  1/16  in.  This  con- 
sistency should  be  observed  in  order  to  have  graded  sizes 
in  the  entire  mixture. 

Rock  dust  was  formerly  considered  objectionable  in  an 
aggregate.  It  is  now  generally  recognized  that  this  is 
very  valuable  in  concrete,  as  it  fills  the  smaller  voids  and 
makes  the  concrete  more  dense.  Of  course,  if  this  dust 
is  rotten  stone  ground  up,  it  should  be  screened  out.  If 
the  rock  dust  is  not  uniformly  distributed  it  may  be  best 
to  screen  it  out  and  use  it  as  sand. 

The  aggregate  for  small  work  should  have  small  sizes 
of  stone.  In  reinforced  concrete  beams  and  columns  the 
maximum  size  of  stones  should  generally  be  %  in.  to  I  in. 
In  arches  a  good  size,  if  no  small  meshes  are  employed  in 
the  steel  reinforcement,  is  2  in.  to  21/&  in.  The  reason 
that  the  stones  should  be  small  is  so  that  they  will  pack 
around  the  reinforcement  and  not  leave  voids.  In  walls 
and  heavy  work  large  sized  stones  are  not  objectionable. 
Rubble  concrete,  sometimes  called  cyclopean  concrete,  is 
concrete  in  which  large  stones  are  embedded.  These  may 
be  almost  any  size  convenient  to  handle.  They  should 
not  be  placed  near  the  surface  or  close  to  each  other. 
Rubble  concrete  is  used  in  massive  work.  In  some  con- 
crete work  large  boulders  are  placed  against  the  forms 
for  appearance,  to  give  a  rustic  look. 

The  weight  of  broken  limestone  per  cu.  ft.  is  about  85 
to  95  Ib.  or  about  2300  to  2600  Ib.  per  cu.  yd.  Gravel  and 
broken  trap  weigh  2800  to  3000  Ib.  per  cu.  yd. 

42 


Cinders  are  often  made  use  of  in  concrete.  Cinder  con- 
crete is  very  useful  in  filling  in  between  the  sleepers  in 
buildings.  It  could  also  be  made  use  of  in  filling  in  the 
spandrel  of  a  stone  or  concrete  arch.  If  the  cinders  are 
well  burned  and  free  from  lumps  of  coal,  cinder  concrete 
makes  an  excellent  fire  protection.  It  is  light  in  weight 
and  porous  and  a  very  poor  conductor  of  heat.  It  has 
the  further  advantage  that  nails  can  be  driven  into  it 
with  ease  for  a  month  or  two  after  it  has  set.  Cinder 
concrete  is  not  very  strong.  Cinders  usually  contain  much 
sulphur.  Steel  laid  in  cinders,  if  moisture  be  present 
will  rapidly  corrode,  on  account  of  the  formation  of  sul- 
phuric acid,  due  to  oxidation  of  the  sulphur  and  addition 
of  water.  Iron  or  steel  pipe  laid  in  a  cinder  fill  should 
be  surrounded  by  concrete  or  at  least  by  clay.  Cinder 
concrete  1 :2 14,  mixed  wet,  is  probably  as  good  a  protec- 
tion for  steel  as  stone  concrete.  Cinders  for  concrete 
should  be  clean.  It  is  sometimes  necessary  to  wash  them 
and  to  sift  out  the  ashes  as  well  as  to  break  up  the  large 
clinkers. 

In  some  localities  there  are  large  deposits  of  shells, 
which,  mixed  with  sand  and  cement,  make  a  good  con- 
crete. Tests  of  any  such  substances  should  be  made  to 
determine  the  best  mixture  and  the  strength. 

Slag  is  used  to  some  extent  in  making  concrete.  Or- 
dinary broken  slag  does  not  seem  to  be  a  desirable  aggre- 
gate on  account  of  its  unstable  chemical  composition. 
This  is  especially  true  of  fresh  slag.  Seasoning  may  dis- 
solve out  the  undesirable  chemical  compounds.  When 
molten  slag  is  run  into  water,  it  is  granulated,  and  much 
of  the  objectionable  sulphur  is  washed  out.  Pulverized 
and  mixed  with  slaked  lime  alone  this  granulated  slag 
can  be  made  into  bricks  or  blocks. 

Crushed  marble  is  employed  in  the  manufacture  of  some 
brands  of  artificial  stone.  This  may  be  mixed  with  ce- 
ment alone. 


43 


Mortar. 

Mortar  may  be  lime  and  sand,  neat  cement,  cement  and 
sand,  or  cement,  lime  and  sand. 

Lime  mortar  is  made  of  one  part  of  lime  paste  to  about 
3  or  4  parts  of  sand.  The  New  York  Building  Code  gives 
1 :4  as  the  proportion.  The  volume  of  the  resulting  mortar 
is  about  equal  to  that  of  the  sand.  Common  lime  mortar 
will  not  set  in  water.  It  takes  a  long  time  for  it  to  set 
in  a  damp  place.  If  air  is  excluded,  it  will  never  set. 
Nevertheless  some  water  is  required  in  the  setting  process, 
and  lime  mortar  suddenly  dried  will  be  killed.  Hence 
it  is  well  to  moisten  bricks  before  they  are  laid  in  lime 
mortar,  especially  if  they  are  porous.  Lime  mortar  should 
not  be  used  in  very  thick  walls  or  in  very  thick  joints; 
also  it  is  unsuitable  for  making  concrete.  The  reason  for 
this  is  twofold:  in  the  first  place  air  must  have  access  to 
the  mortar  to  harden  it;  in  the  second  place  the  small  ten- 
sile strength  of  the  mortar  makes  it  weak  to  resist  lateral 
flow,  and  it  is  consequently  of  little  use  in  overcoming 
compression  in  a  mass.  The  ultimate  tensile  strength  of 
lime  mortar  is  about  20  to  50  Ibs.  per  sq.  in.  The  com- 
pressive  strength  depends  largely  upon  the  thinness  of 
the  joints.  Cubes  of  mortar,  when  tested  in  compression 
stand  but  little;  but,  when  the  sand  is  confined  in  joints 
between  bricks  or  stone,  the  adhesive  strength  of  the  ce- 
menting lime  is  taxed  less,  hence  a  greater  crushing 
strength  can  be  withstood.  The  report  of  tests  made  in 
1884  at  the  Watertown  Arsenal  show  cubes  of  lime  mor- 
tar to  stand  120  Ibs.  per  sq.  in.  in  crushing.  The  same 
report  shows  brick  piers  built  with  lime  mortar  to  stand 
from  about  1000  Ibs.  to  2000  Ibs.  per  sq.  in.  The  strength 
of  a  wall  laid  in  lime  mortar  will  be  gaged  not  so  much 
by  the  strength  of  the  brick  as  by  that  of  the  mortar, 
since  lime  mortar,  even  confined  in  joints,  is  only  about 
one-tenth  to  one-fifth  as  strong  as  ordinary  brick.  Lime 
mortar  requires  about  a  month  to  set  sufficiently  to  re- 
ceive any  considerable  load,  but  it  continues  to  harden 

44 


indefinitely.  In  plasters,  gypsum  or  plaster  of  Paris  is 
often  added  to  hasten  the  setting.  Dry  and  thoroughly 
set  lime  mortar  weighs  about  no  Ibs.  per  en.  ft. 

Lime  mortar  is  greatly  improved  by  adding  cement, 
either  Rosendale  or  Portland.  The  strength  is  increased, 
and  the  time  of  setting  is  shortened.  On  the  other  hand 
cement  mortar  for  brick  or  stone  work  is  improved  by 
the  addition  of  lime.  It  is  made  easier  to  work  with  the 
trowel ;  it  does  not  set  up  so  quickly,  giving  more  time 
to  place  it;  the  adhesive  value  is  improved  on  such  sur- 
faces as  concrete  blocks.  A  common  mixture  is  that  of 
equal  volumes  of  I  to  3  lime  mortar  and  i  to  3  cement 
mortar.  The  mixture  of  the  two  mortars  is  called  cement 
and  lime  mortar.  Lime  paste  or  hydrated  lime  may  be 
added  to  cement  mortar  without  being  first  mixed  with 
sand.  The  addition  of  10  to  25  per  cent,  of  lime  paste 
to  cement  mortar  will  decrease  its  permeability  and  makes 
it  more  adherent  to  old  concrete  and  to  concrete  blocks. 
Lime  paste  is  used  in  making  some  artificial  stone,  of 
sand  and  cement,  to  increase  the  density. 

The  addition  of  10  to  20  per  cent,  of  hydrated  lime  does 
not  destroy  the  hydraulic  property  of  Portland  cement. 
Cement  mortar  to  which  lime  is  added  will  attain  greater 
strength  when  stored  in  water,  after  a  day  or  two  in 
air,  than  when  kept  in  air  only.  Mr.  H.  B.  Nichols,  in  a 
letter  in  Eng.  News,  Dec.  5,  1907,  describes  some  tests 
on  adding  lime  paste  to  I  -.3  Portland  cement  mortar  and 
i  :2  natural  cement  mortar.  It  was  found  that  from  4  to 
20  per  cent,  of  lime  paste  added  to  natural  cement  mor- 
tar increased  the  strength  on  an  average  25  per  cent. 
Percentages  of  lime  below  20  did  not  seriously  weaken 
Portland  cement  mortar;  greater  percentages  did  weaken 
it.  The  briquettes  required  to  be  kept  in  air  48  hours 
before  being  stored  in  water.  Lime  increased  the  adhesion 
of  mortar  very  materially. 

Tests  from  the  Government  report  above  referred  to 
for  blocks  of  cement  and  lime  mortar,  one  part  cement 
mortar  and  two  of  lime  mortar,  showed  a  strength  in 
45 


compression  of  175  to  200  Ibs.  per  sq.  in.,  Portland  and 
Rosendale  cement  showing  about  equal  strength.  Brick 
piers  in  similar  mortar  showed  a  compressive  strength  of 
about  1500  Ibs.  per  sq.  in. 

Cement  without  sand,  or  neat  cement,  is  not  very  often 
made  use  of.  It  is,  however,  useful  in  setting  anchor 
bolts  in  drilled  holes  in  stone  work  and  is  considered  bet- 
ter than  lead  or  sulphur  for  this  purpose.  The  ultimate 
adhesive  strength  is  about  400  to  500  Ibs.  per  sq.  in.  of 
surface  of  bolt  in  contact  with  cement.  Blocks  of  neat 
Portland  cement  about  2  years  old  showed  a  compressive 
strength  of  about  5000  Ibs.  per  sq.  in.  Broad,  flat  blocks 
showed  a  strength  two  or  three  times  as  great  (Govt. 
Report,  1884),  showing  that  in  joints  between  bricks  the 
crushing  strength  of  neat  Portland  cement  is  ten  to  fif- 
teen thousand  pounds  per  sq.  in.,  or  about  the  strength 
of  good  hard  brick. 

A  series  of  tests  that  serve  to  show  not  only  the  ten- 
sile strength  of  neat  cement  of  the  average  American 
brand  but  also  the  quality  of  the  cement  and  the  strength 
of  1 13  mortar  is  that  made  in  1900  by  the  Dept.  of  Public 
Works  of  Philadelphia  on  8  different  brands  of  Ameri- 
can Portland  cement.  In  all  over  4000  tests  were  made. 
The  averages  of  the  results  from  the  different  brands  are 
as  follows : — 

99.4%  passed  through  a  No.  50  sieve. 

90.3%  passed  through  a  No.  100  sieve. 

75.6%  passed  through  a  No.  200  sieve. 

Specific  gravity,  3.124. 

Time  of  initial  set,  73.6  minutes. 

Time  of  hard  set,  358.2  minutes. 

Rise  of  temp,  of  paste  in  setting,  5.4  degrees. 


46 


Ultimate  Tensile  Strength.  Pounds  per  Square  Inch. 

1  13  Std. 
Quartz  Sand 
Neat. 

1  day  449  88 
7  days                                     724                                     234 

28  days  792  311 

2  mos.  792  323 

3  mos.  803  327 

4  mos.  831  329 
6  mos.                                    818                                    333 

A  later  summary  of  average  results  of  cement  tests 
made  in  the  Philadelphia  laboratories  is  the  following 
given  by  Mr.  E.  S.  Lamed  in  a  paper  read  before  the  A. 
A.  P.  C.  M.,  Atlantic  City,  N.  J.  Sept.  1907. 

Proportions  Tensile  Strength,  Ib.  per  sq.  in. 


7 

28 

2 

3 

4 

6 

12 

days 

days 

mos. 

mos. 

mos. 

mos. 

mos. 

Neat 

cement 

710 

768 

760 

740 

732 

758 

768 

i  to 

i 

mortar 

590 

692 

690 

680 

680 

685 

695 

i  to 

2 

mortar 

370 

458 

460 

455 

453 

458 

460 

I  to 

3 

mortar 

208 

300 

310 

310 

3io 

310 

308 

i  to 

4 

mortar 

130 

2TO 

230 

230 

230 

232 

232 

i  to 

5 

mortar 

80 

150 

185 

195 

195 

195 

197 

The  above  tabulation  was  interpolated  from  the  dia- 
gram of  cement  mortar  tests  prepared  by  Mr.  W.  Purves 
Taylor.  The  results  of  the  neat  tests  and  the  1  13  mortar 
tests  (i.  e.  one  part  cement  to  three  parts  crushed  quartz, 
by  weight)  are  averaged  from  over  100,000  tests,  while  the 
other  results  are  based  on  from  300  to  500  tests.  (See 
Concrete,  Oct.  1907.) 

One  volume  of  Portland  cement,  measured  loose,  mixed 
with  one-third  of  a  volume  of  water  will  shrink  to  .78 
of  a  volume  of  stiff  cement  paste.  A  volume  of  Rosen- 
dale  cement  and  .4  of  a  volume  of  water  will  make  about 
the  same  amount  of  paste  as  the  Portland.  It  takes  6.75 
bbl.  of  cement  to  make  one  cu.  yd.,  measured  loose,  hence 

47 


a  cu.  yd.  of  cement  paste  would  require  8.65  bbl.  of  ce- 
ment. This  is  on  the  basis  of  4  cu.  ft  to  a  barrel  of  ce- 
ment. A  bag  or  quarter  barrel  of  cement  is  accepted  by 
many  engineers  as  a  cubic  foot.  Sample  bags  should  be 
measured  and  weighed  to  see  that  this  holds  true. 

The  office  of  cement  in  mortar  is  to  fill  the  voids  in 
the  sand  and  at  the  same  time  cement  the  particles  to- 
gether. The  voids  in  sand  are  about  one-third  of  the  vol- 
ume. A  mixture  of  one  part  of  cement  to  three  of  sand 
will  therefore  give  a  correct  proportion  on  this  basis  and 
result  in  a  volume  of  mortar  not  much  if  any,  more  than 
that  of  the  sand.  This  is  the  common  mixture  for  ce- 
ment mortar.  The  richer  the  mortar  in  cement  the  great- 
er will  be  its  tensile  strength.  The  compressive  strength 
does  not  increase  in  the  same  proportion,  but  depends  some- 
what on  the  thinness  of  the  joints.  For  brick  work  or 
cut  stone  work  there  is  no  advantage  in  using  richer  mor- 
tar than  i  -.3  if  the  wall  is  to  be  in  compression  only.  In 
concrete  or  rubble  work  richer  mortar  by  its  greater  ten- 
sile strength  prevents  lateral  failure  under  compressive 
stresses. 

Richer  mortar  than  i  :3  will  occupy  more  space  than  the 
volume  of  the  sand.  One  volume  of  average  sand  can  be 
estimated  to  give  one  volume  of  1 13  mortar ;  0.9  volume 
of  sand  can  be  estimated  to  give  one  volume  of  i  :2  mortar ; 
0.7  volume  of  sand  will  give  one  volume  of  1:1  mortar. 
One  cu.  yd.  of  1 13  mortar  will  require  about  2*/4  bbl.  of 
Portland  cement ;  one  cu.  yd.  of  1 12  mortar  will  require 
about  3  bbl.  of  cement;  one  cu.  yd.  of  1:1  mortar  will  re- 
quire about  4.7  bbl.  of  cement. 

Mortars  are  generally  mixed  by  volume  in  actual  con- 
struction. In  laboratory  tests,  for  greater  accuracy,  the 
quantities  are  usually  measured  by  weight. 

Brick  work  with  %"  joints  requires  about  one-eighth 
of  the  volume  in  mortar.  For  %"  to  W  joints  about  20 
per  cent,  will  be  mortar.  Ashlar  masonry  requires  about 
6  to  8  per  cent,  of  the  volume  in  mortar,  and  rubble  ma- 
sonry requires  25  to  40  per  cent,  of  mortar. 
48 


The  amount  of  water  required  is  about  one-fourth  the 
volume  of  the  cement  in  neat  cement  or  about  one-half 
of  the  volume  of  the  cement  in  sand  and  cement  mortar. 

Portland  and  Rosendale  cements  may  be  mixed  in  any 
proportion  in  mortar.  If  equal  quantities  of  each  be  used, 
the  strength  will  be  about  the  mean  between  that  of  the 
separate  mortars,  but  it  will  set  in  about  the  time  re- 
quired for  Rosendale  cement. 

As  in  the  case  of  lime  mortar,  mortar  made  of  cement 
and  sand  will  stand  much  greater  crushing  load  in  the 
thin  joints  of  a  brick  wall  than  in  cubes.  The  strength 
in  the  thin  joint  is  sometimes  many  times  as  much  as  the 
same  mortar  in  a  cube.  Good  1 13  Portland  cement  mortar 
in  thin  joints  will  generally  withstand  the  pressure  that 
will  crush  the  strongest  brick  or  stone. 

Mortar  made  with  crusher  dust,  that  is,  stone  dust  that 
results  in  the  crushing  of  stone,  was  found  by  Govern- 
ment tests  to  be  superior  in  tensile  strength  both  to  sand 
and  crushed  quartz.  In  the  report  of  the  Chief  of  Engin- 
eers, U.  S.  A.,  for  1902  (See  Eng.  News,  Apr.  2,  1903) 
the  following  results  of  tests  are  shown. 
First  Series  of  Tests. 


Sand 
I 

2 

3 

i 

2 

3 
I 

2 

3 


of 

Tests 

> 

i 

'•3 

i  Period 

Age 

24  hrs. 

7  da. 

i  mo. 

3  mo. 

6  mo. 

i  yr. 

14 

103 

370 

397 

376 

381 

355 

36 

105 

241 

274 

294 

290 

291 

12 

79 

397 

544 

6o7 

628 

602 

14 

53 

243 

282 

266 

259 

227 

36 

65 

169 

198 

207 

192 

185 

12 

37 

267 

395 

494 

512 

484 

i:5 

14 

31 

187 

221 

211 

190 

161 

36 

36 

132 

155 

159 

145 

144 

12 

25 

211 

336 

428 

421 

416 

49 


Second   Series  of  Tests. 
No.  of  No.  of  Tests,  1 13 


Sand  Each  Period 

Age 

24  hrs. 

7  da. 

i  mo. 

3  mo. 

6  mo. 

i 

12 

62 

302 

425 

449 

436 

2 

12 

58 

224 

289 

310 

310 

3 

12 

III 

399 

505 

603 

593 

I 

12 

17 

153 

283 

329 

325 

2 

12 

23 

136 

193 

220 

234 

3 

12 

60 

287 

411 

453 

501 

f»3b?r  12  9          103          189          244          263 

2  12  7  85          130          168          184 

3  12  34         212          322          377         429 

Notes.  No.  i,  standard  crushed  quartz;  No.  2,  Plum 
Island  sand;  No.  3,  crusher  dust.  Proportions  are  of 
Portland  cement  to  sand  by  volume.  In  first  series  of 
tests  mortar  was  quite  wet;  in  second  series  consistency 
was  medium.  Values  in  table  are  ultimate  tensile  strength 
in  Ibs.  per  sq.  in. 

Some  tests  given  by  Mr.  G.  J.  Griesenauer  in  Eng.  News, 
Apr.  16,  1903  show  limestone  screenings  to  be  superior 
to  sand  in  bricquettes  tested  in  various  periods  from 
seven  days  to  one  year.  Bricquettes  made  of  screenings 
as  lean  as  1 13  showed  greater  tensile  strength  at  the  end 
of  one  year,  in  some  cases,  than  neat  Portland  cement. 

Unlike  lime  mortar  cement  mortar  will  set  in  fresh 
water  or  sea  water  or  entirely  excluded  from  air  or  water, 
except  the  water  used  in  mixing.  Some  substances,  how- 
ever, will  cause  cement  mortar  or  concrete  to  disintegrate 
while  setting.  Water  containing  the  discharge  from  a 
pulp  mill  was  found  in  one  case  to  cause  setting  concrete 
to  become  absolutely  worthless.  (See  Eng.  News,  Feb.  5, 
1903).  Manure,  especially  if  it  be  wet,  will  rot  concrete 
while  it  is  setting,  but  does  not  seem  to  affect  concrete 
that  is  set  and  hardened.  (See  Eng.  News,  Jan.  I,  1903, 

oO 


p.  ii ;  Jan.  29,  1903,  p.  104;  Feb.  5,  1903,  p.  127).  Manure 
is  sometimes  used  and  recommended  to  prevent  concrete 
from  freezing.  This  is  bad  practice,  if  the  manure  is 
placed  in  contact  with  the  concrete.  It  is  not  only  liable 
to  rot  setting  concrete,  but  it  will  discolor  it.  Weak  acids 
will  attack  the  lime  in  mortar  or  concrete  that  is  setting. 

The  effect  of  oil  on  concrete  is  not  well  understood. 
In  Eng.  News,  Vol.  53,  p.  279  and  Vol.  58,  p.  16,  some 
tests  are  reported  which  show  that  most  oils  have  a  de- 
leterious effect  on  concrete.  Concrete  or  mortar  that  is 
setting  is  especially  susceptible  to  the  weakening  influ- 
ence of  oils.  Animal  and  vegetable  fats  and  oils  are  the 
most  harmful,  excepting  such  drying  oils  as  boiled  linseed. 
This  latter,  while  it  penetrates  concrete  to  some  extent 
does  not  appear  to  weaken  it.  Petroleum  does  not  seem 
to  injure  concrete.  Mr.  H.  T.  Poe,  Jr.  in  Engineering 
Record,  Vol.  55,  p.  222  tells  of  a  reservoir  painted  inside 
with  coal  tar  which  was  used  for  fuel  oil  and  gave  satis- 
faction. An  experimental  tank  of  1 :2 14  concrete,  not 
treated,  with  fuel  oil  in  9  months  showed  no  disintegra- 
tion and  no  leaks,  only  discoloring  of  concrete  for  1^4  in. 
(Eng.  Record,  Vol.  55,  p.  9.)  Tanks  not  treated  were  also 
found  to  be  unaffected  by  petroleum  and  petroleum  pro- 
ducts by  Mr.  J.  L.  Gray  (Eng.  Record,  Vol.  55,  p.  313.) 
See  Eng.  News,  Vol.  57,  p.  13,  where  test  of  i  :2 14  con- 
crete tank  filled  with  fuel  oil  gave  satisfactory  results. 
Oil  penetrated  concrete  less  than  %  in.  See  also  Eng. 
News,  Vol.  53,  p.  279,  and  Eng.  Record,  Vol.  51,  p.  357. 

Alternate  freezing  and  thawing  during  setting  destroys 
weaker  mortars,  such  as  lime  mortar  or  Rosendale  cement 
mortar.  Some  experimenters  have  reported  that  it  does 
not  affect  the  strength  of  Portland  cement  mortar.  It 
is  the  general  opinion,  however,  that  it  is  harmful  to  any 
setting  mortar  or  concrete.  Freezing  delays  the  setting 
of  mortar,  but  if  thawing  does  not  occur  until  the  mortar 
is  set,  it  does  not  seem  to  weaken  it.  The  setting  of  mor- 
tar is  sometimes  entirely  suspended  due  to  its  being 
frozen.  Upon  thawing  the  setting  resumes.  Concrete  in 

51 


foundations  has  been  found,  after  having  stood  for  some 
time  in  freezing  weather,  to  quake;  then,  after  having 
time  to  set  in  warmer  temperature,  it  has  become  good 
and  hard.  Freezing  is  particularly  harmful  when  there 
is  a  mortar  finish  on  concrete  poorer  in  cement,  or  where 
the  facing  is  a  richer  mixture  than  the  body  of  a  wall. 
The  rich  mortar  is  apt  to  break  off  from  the  main  body. 
Brick  walls  in  mortar  should  not  be  run  up  too  fast  in 
freezing  weather.  The  heavy  load  coming  upon  the  lower 
parts  of  walls  thus  built  have  caused  many  failures  on 
account  of  the  fact  that  the  mortar  had  frozen  and  not 
set.  When  the  frozen  mortar  thawed  it  was  almost  in  the 
condition  of  fresh  mortar.  Failures  have  also  occurred 
in  concrete  work  on  account  of  the  fact  that  centers  were 
removed  from  work  that  was  frozen  and  not  set. 

In  a  paper  by  Messrs.  P.  L.  Barker  and  H.  A.  Seymonds, 
published  in  Eng.  News,  May  2,  1895,  a  number  of  testa 
are  given  on  the  strength  of  cement  mortars  subjected  to 
freezing  temperature.  These  experimenters  found  that 
Portland  cement  mortar  suffers  no  surface  disintegration 
under  any  condition  of  freezing,  but  the  strength  is  di- 
minished, sometimes  very  materially;  Rosendale  cement 
mortar  disintegrates  on  the  surface,  but  seems  to  acquire 
greater  strength  in  the  part  not  disintegrated ;  the  cohesion 
of  Rosendale  cement  mortar  is  destroyed  by  immersion 
in  water  which  freezes  around  it;  salt  used  in  mixing 
water  (about  7  per  cent.)  helps  Rosendale  cement  mor- 
tar to  resist  surface  disintegration,  but  appears  to  dimin- 
ish the  strength ;  a  mixture  of  Portland  and  Rosendale 
cements  was  found  to  combine  the  good  points  of  each, 
namely,  to  resist  surface  disintegration  and  not  to  lose  its, 
strength  due  to  freezing;  lime  mortar  kept  frozen  until 
it  had  time  enough  to  set  was  not  injured,  but  when  al- 
ternately frozen  and  thawed  it  disintegrated. 

Salt  in  the  water  is  sometimes  used  to  prevent  freezing 
of  mortar.  On  exposed  walls  salt  is  liable  to  produce 
effloresence  and  to  disfigure  the  wall.  Moist  salt  is 
known  to  corrode  steel,  so  that  concrete  in  which  steel  is 

52 


embedded,  if  it  contains  salt  and  becomes  wet,  may  cor- 
rode the  steel.  Whether  or  not  the  steel  is  safe  from  cor- 
rosion if  the  concrete  is  kept  dry  is  a  matter  of  uncer- 
tainty. Heavy  walls  in  plain  concrete  do  not  need  salt 
in  the  mixture,  unless  it  be  in  extremely  low  temperature, 
for  the  cement  in  setting  generates  heat.  Salt  may  be 
found  useful  in  such  thin  unreinforced  work  as  sidewalks. 
The  use  of  such  substances  as  salt,  sugar,  soft  soap,  etc., 
sometimes  resorted  to  for  various  purposes,  seems  to  be 
of  doubtful  benefit.  At  least  the  effect  of  these  substances 
is  not  clearly  understood. 

Heating  the  materials  of  mortar  or  concrete  before  mix- 
ing is  very  often  practiced  and  is  very  often  recommended 
to  prevent  freezing.  Experiments  have  shown  that  it  is 
harmful  to  use  hot  or  even  warm  materials.  Mr.  Wm. 
M.  Maclay,  in  Trans.  Am.  Soc.  C.  E.,  Vol.  VI,  1877,  de- 
scribes tests  in  which  the  heating  of  ingredients  of  cement 
mortar  to  100  deg.  F.  reduced  the  strength  to  only  7  to  30 
per  cent,  of  that  of  specimens  made  at  40  deg.  F.  Experi- 
ments made  by  the  Austrian  Society  of  Engineers  and 
Architects  (See  Eng.  News,  Vol.  31,  p.  253)  led  to  the  con- 
clusion that  mortar  mixed  with  warm  water  shows  about 
the  same  deterioration  in  freezing  temperature  as  when 
cold  water  is  used. 

The  only  warrant  for  the  use  of  hot  materials  seems  to 
be  the  very  doubtful  one  that  it  is  often  done.  The  only 
evidence  that  it  is  not  harmful  as  practiced  appears  to  be 
the  negative  evidence  that  no  failures  have  been  traced  to 
the  use  of  hot  materials.  Pleat  increases  the  activity  of  ce- 
ment, and  quick  setting  of  mortar,  that  is,  setting  during 
the  process  of  placing,  is  detrimental  to  its  strength. 
Heat  drives  off  water  the  presence  of  which  is  necessary 
to  the  proper  hardening  of  the  cement.  Concrete  bricks 
or  blocks  are  sometimes  steam  cured,  but  in  this  case, 
the  heat  is  applied  after  the  concrete  is  placed  in  the 
forms  and  not  before  it  is  handled  in  a  plastic  state.  The 
steam  immersion  would  not  take  away  water  from  the 
concrete,  but  would  rather  add  to  that  already  there  by 

53 


condensation,  unless  the  blocks  were  heated  by  other  means 
hotter  than  the  steam.  In  doing  concrete  work  in  hot 
weather  it  is  desirable  to  keep  the  materials  cool  and  the 
concrete  protected  from  the  direct  rays  of  the  sun.  These 
adverse  conditions  should  not  be  artificially  produced  in 
cold  weather. 

The  safest  and  best  materials  for  concrete  are  good, 
clean,  hard  broken  stone  or  gravel,  good  clean  coarse 
sand,  finely  ground  Portland  cement  of  known  quality, 
and  good  clean  fresh  water.  The  best  temperature  for 
these  materials  is  as  cool  as  they  can  be  kept  without  Be- 
ing below  freezing. 

As  stated,  water  for  use  in  making  mortar  or  concrete 
should  be  clean.  It  should  not  be  water  from  coal  mines. 
It  should  not  contain  sewage  or  rotting  substances.  It 
should  not  contain  waste  from  pulp  mills  and  should  not 
be  acid  in  reaction.  Sea  water  for  concrete  is  doubtful. 
It  should  not  be  used,  if  fresh  water  can  be  obtained. 

The  mixing  of  mortar  should  be  thorough.  If  done  by 
hand,  the  sand  should  be  placed  on  the  mixing  board  and 
spread  out  to  an  even  thickness  of  about  2  or  3  inches. 
Upon  this  the  cement  should  be  evenly  spread  and  the 
dry  materials  turned  over  three  or  four  times  with  shovels. 
Water  is  then  added.  It  should  not  be  dashed  on  so  as 
to  wash  away  the  cement.  After  the  addition  of  the  water 
the  mortar  should  be>  turned  until  the  pile  is  uniform 
throughout  both  in  color  and  in  consistency. 

Machine  mixing,  both  of  mortar  and  concrete,  generally 
results  in  a  more  uniform  product  than  hand  mixing. 
There  are  two  general  classes  of  mixers,  namely,  batch 
mixers  and  continuous  mixers.  In  the  batch  mixer  the 
materials  for  one-half  to  one  cubic  yard  are  put  in  at 
once,  and  this  is  turned  over  until  all  are  uniformly  mixed, 
then  the  whole  is  discharged.  In  a  continuous  mixer  the 
various  materials  are  fed  regularly  into  the  mixer,  and 
concrete  is  discharged  continuously. 

Thorough  mixing  and  uniformity  of  product  are  the 
prime  essentials.  There  should  be  in  any  given  quantity, 

54 


say  a  shovelful  or  a  wheelbarrow  full,  just  the  amount 
called  for  of  the  several  materials.  If  1 :2 14  concrete  is 
called  for,  there  should  be  one  part  of  cement,  two  parts 
of  sand,  and  four  parts  of  broken  stone  or  gravel  in 
each  such  quantity  throughout.  This  is  true  of  the  amount 
of  water  used  as  well  as  other  ingredients.  Each  batch 
and  every  part  of  the  batch  should  be  of  the  same  con- 
sistency. If  this  thoroughness  and  uniformity  are  not 
maintained,  the  resulting  concrete  will  not  be  homogene- 
ous. 

In  a  batch  mixer  it  is  not  difficult  to  secure  uniformity 
as  to  amounts  of  ingredients  in  each  batch,  if  a  careful 
man  is  placed  in  charge.  There  are,  however,  practical 
difficulties  in  measuring  the  materials.  One  of  these  is 
the  fact  that  the  most  convenient  thing  to  haul  sand  and 
stone  from  the  pile  is  a  wheelbarrow,  and  it  is  very  diffi- 
cult to  gage  the  capacity  of  a  wheelbarrow  or  to  get  work- 
men to  load  one  the  same  amount  at  each  trip. 

It  is  quite  evident  that  to  make  three  or  four  different 
streams  discharge  proportionate  amounts  of  materials,  as 
must  be  done  in  a  continuous  mixer,  is  fraught  with 
many  difficulties  and  difficulties  that  are  harder  to  over- 
come than  the  measuring  of  material  before  they  are  put 
into  a  batch  mixer.  Continual  vigilance  is  necessary  in 
order  to  make  sure  that  none  of  the  various  streams  be- 
come clogged  or  fail  to  discharge  their  proper  amounts  of 
material. 

Cement  mortar  should  not  be  mixed  in  large  batches, 
if  it  will  require  long  to  use  up  the  batch.  It  should  be 
fresh  mixed  and  used  as  soon  after  mixing  as  possible, 
as  it  begins  to  take  on  its  initial  set  in  a  short  time.  If 
it  is  necessary  to  leave  mortar  stand  a  while,  it  should  be 
re-tempered,  adding  a  little  water  if  necessary,  before  it  is 
used.  It  is  said  that  re-tempered  mortar  will  adhere  bet- 
ter to  old  concrete  surfaces  or  to  concrete  blocks  than 
fresh  mortar.  For  the  same  reason  re-tempered  concrete 
might  be  found  useful  in  joining  to  old  work  or  to  con- 
crete that  has  partially  set. 

55 


Re-tempering  of  mortar  and  concrete  are  usually  pro- 
hibited because  of  the  uncertainties  attending  the  prac- 
tice. 

Rosendale  cement  mortar  and  concrete  are  injured  to 
a  greater  extent  by  re-tempering  or  by  delay  in  placing 
than  Portland  cement  mortar  and  concrete.  This  is  be- 
cause Rosendale  cement  takes  its  initial  set  in  a  shorter 
time  than  Portland.  Experiments  reported  by  Mr.  Thos. 
S.  Clark  and  published  in  Eng.  Record,  Dec.  27,  1902,  show 
that  Rosendale  cement,  neat  and  with  sand,  if  re-tempered 
by  adding  water,  after  allowing  to  stand  for  one  hour,  is 
reduced  in  tensile  strength  about  50  per  cent,  for  long- 
time tests.  For  tests  which  set  but  a  few  days  greater 
weakness  than  this  was  shown  for  neat  cement  though 
not  so  much  difference  for  tests  with  sand.  The  same 
report  states  that  no  marked  difference  was  shown  in  the 
case  of  Portland  cement  re-tempered  after  one  hour.  It 
is  probable,  however,  that  Portland  cement  re-tempered 
after  several  hours  standing  would  show  similar  weak- 
ness. 

Continuous  mixing  of  cement  mortar  for  several  hours 
seems  to  cause  it  to  retain  its  life,  that  is;  it  seems  to  re- 
tard its  setting.  Some  experiments  reported  by  Mr.  G. 
Y.  Skeels,  in  Eng.  News,  Nov.  6,  1902,  show  that  the  ten- 
sile strength  of  Portland  cement  bricquettes  of  15  days 
standing,  after  continuous  mixing  for  9  or  10  hours  was 
reduced  only  about  one-quarter  from  the  freshly  mixed 
cement.  Similar  results  were  found  both  for  neat  ce- 
ment and  i  to  2  mortar. 

Concrete  deposited  under  water  has  been  found  to  be 
better  if  allowed  to  stand  a  few  hours  after  mixing,  as 
the  cement  will  not  leech  out  so  readily. 

One  part  of  brick  dust,  one  part  of  quick  lime,  and  two 
parts  of  sand,  mixed  dry  and  tempered  with  water  will 
make  a  hydraulic  mortar. 

Grout  is  the  name  given  to  thin  or  liquid  mortar.  It 
is  used  for  filling  in  joints  or  spaces  which  cannot  other- 
wise be  reached.  Cast  bases  for  columns  are  usually  left 

56 


rough  on  the  bottom  surface,  and  holes  are  provided  in 
the  bottom  plate  for  grouting.  The  grout  is  prevented 
from  running  away  by  banking  up  sand  around  the  edge 
of  the  base.  Grout  may  be  used  to  strengthen  walls  in 
which  the  mortar  has  washed  out.  It  may  also  be  used 
in  making  concrete  by  first  placing  broken  stone  or  gravel 
and  then  pouring  the  grout  into  the  interstices.  A  fill  of 
broken  stone  or  a  gravel  bed  in  which  there  is  little  or  no 
sand  may  be  consolidated  by  filling  the  voids  with  grout. 

The  method  referred  to  in  the  last  paragraph  of  pouring 
grout  under  the  base  of  a  column  may  be  used  to  ad- 
vantage also  for  bridge  shoes.  It  is  a  good  plan  to  wedge 
up  a  bridge  shoe  an  inch  or  two  above  the  surrounding 
masonry  (allowance  being  made  for  this  in  the  plans), 
and  then  after  having  built  a  dam  of  sand  around  the 
edge,  to  fill  in  under  the  shoe  with  grout.  This  keeps 
water  from  lying  around  the  bridge  shoe. 

In  Eng.  News,  Aug.  8,  1907,  p.  145,  there  is  a  short  de- 
scription of  repairs  made  on  a  bridge  pier  in  Germany 
that  had  been  cracked  horizontally  below  the  water  level 
and  displaced  by  the  action  of  an  ore  steamer.  The  outer 
edges  of  the  crack  were  sealed  by  means  of  wooden  wedges 
and  oakum,  and  in  addition  a  strip  of  canvas  was  placed 
around  the  pier  and  bound  thereto.  Grout  was  pumped 
into  the  crack,  by  means  of  air  pressure  and  grouting 
drums,  through  pipes  provided  for  this  purpose.  The 
grout  was  a  i  to  I  mixture  of  Portland  cement  and  sand, 
mixed  dry  and  then  tempered  with  an  equal  volume  of 
water. 

Concrete. 

Concrete  is  a  mixture  of  mortar  and  some  aggregate, 
hence  what  has  been  said  concering  mortar  and  its  char- 
acteristics has  application  in  a  large  measure  to  concrete. 
The  mortar  with  its  contained  cement,  acts  to  hold  the 
aggregate  together  making  of  the  whole  an  artificial  stone. 
An  ideal  concrete  is  one  in  which  the  cement  fills  or  more 

57 


than  fills  the  voids  in  the  sand  to  form  the  mortar  and 
the  mortar  fills  the  voids  in  the  broken  stone  or  other 
aggregate.  Proportions  in  this  country  are  nearly  always 
given  in  bulk  or  volume. 

The  voids  in  broken  stone  are  about  40  to  50  per  cent, 
of  the  bulk.  Concrete  composed  of  one  part  of  mor- 
tar to  two  of  broken  stone  would  therefore  be  about  right. 
The  volume  will  be  practically  equal  to  that  of  the  broken 
stone.  A  common  mixture  for  walls  and  other  heavy 
work  is  one  part  of  cement,  3  parts  of  sand,  and  6  parts 
of  broken  stone.  For  reinforced  concrete  a  richer  mortar 
is  desirable,  because  of  the  fact  that  the  covering  of  the 
steel  with  cement  must  be  assured,  and  because  the  small- 
er size  of  broken  stone  demands  more  cement  to  cover  the 
parts  of  the  aggregate.  The  standard  mixture  for  rein- 
forced concrete  is  i  part  of  Portland  cement,  2  parts  of 
sand,  and  4  parts  of  broken  stone  or  gravel. 

Leaner  mixtures  are  sometimes  used  in  heavy  work 
where  large  sized  aggregates  can  be  employed.  Such  pro- 
portions as  1:3:7,  1:4:8,  or  even  1:5:10  could  be  used 
where  strength  is  not  an  essential  characteristic.  In- 
cluded in  the  volume  of  the  stone  there  could  be  large 
stones,  say  a  foot  or  so  across.  These  should  be  separated 
from  each  other  and  from  the  surface. 

In  general  as  few  different  mixtures  of  concrete  as  pos- 
sible should  be  specified  on  one  contract,  and  the  line  of 
separation  should  be  well  defined,  so  as  to  avoid  confusion. 
The  body  of  a  pier  or  abutment  could  be  of  i  :3 :6  con- 
crete and  the  coping,  because  of  the  need  of  stronger  con- 
crete to  take  the  bridge  seats,  could  be  of  1 :2  -.4  concrete. 
Some  steel  reinforcement  in  the  coping  of  such  a  pier 
would  not  be  out  of  place,  to  tie  it  together  and  prevent 
cracking  in  the  entire  pier.  It  would  not  be  well  to  call 
for  beams  of  one  mixture  and  slabs  or  columns  of  an- 
other, though  column  footings  and  columns  might  be  of 
different  mixtures  if  one  were  plain  and  the  other  rein- 
forced. 

58 


In  ordinary  work  it  is  best  to  specify  standard  mix- 
tures for  the  concrete  and  to  see  that  the  materials  are 
regular,  the  sand  and  aggregate  well  graded  in  size  and 
uniformly  mixed.  It  would  not  be  discreet  to  leave  to 
the  contractor  the  determination  of  the  proportion  of  in- 
gredients. On  special  work  or  very  large  contracts,  where 
the  engineer  is  given  discretion,  he  may  determine  the 
mixtures  that  suit  more  accurately  the  materials  to  be 
used.  The  percentage  of  voids  may  be  ascertained  by 
taking  a  vessel  of  known  capacity  and  filling  it  with  the 
aggregates.  Then  by  weighing  it  before  and  after  filling 
level  full  of  water  the  volume  of  water  may  be  found 
from  the  known  weight  per  cubic  foot  of  water,  namely, 
62.4  Ib.  The  percentage  that  this  volume  of  water  is  of 
the  full  capacity  of  the  vessel  is  the  percentage  of  voids  in 
the  aggregate.  The  same  may  be  done  with  the  sand.  By 
using  about  10  per  cent,  more  cement  than  the  voids  in 
the  sand  and  10  per  cent,  more  sand  than  the  voids  in 
the  broken  stone  a  mixture  will  be  effected  that  is  most 
economical  for  the  given  materials. 

For  quartz  sand  the  voids  may  be  found  by  weighing 
a  known  volume.  The  specific  gravity  of  quartz  is  2.65, 
and  the  weight  per  cu.  ft.  is  165.4  Ibs.  If  then  a  cu.  ft.  of 
sand  weighs  say  100  Ibs.  the  difference,  or  65.4  Ibs.  repre- 
sents the  voids.  Dividing  65.4  by  165.4  we  have  40  as  the 
percentage  of  voids. 

One  way  that  is  recommended  for  finding  the  proper 
mixture  of  sand  and  stone  or  sand  and  gravel  is  based 
on  the  fact  that,  other  things  being  equal,  the  denser  the 
mixture  the  stronger  will  be  the  concrete.  The  operation 
is  that  of  finding  the  mixture  that  has  the  maximum 
weight  for  a  given  volume.  A  common  galvanized '  iron 
pail  and  spring  balances  may  be  used  for  the  purpose. 
The  bucket  is  filled  half  full  of  water,  and  a  batch  of  the 
sand  and  aggregate  at  a  trial  proportion  is  thoroughly 
mixed  and  slowly  dropped  from  a  shovel.  The  surplus 
water  is  allowed  to  flow  over.  Without  tamping  the 
bucket  is  filled  level  full.  The  mixture  that  weighs  the 

oi) 


most  will  give  the  densest  and  strongest  concrete,  and  on 
account  of  having  the  least  percentage  of  voids  it  will  re- 
quire the  least  amount  of  cement. 

Sometimes  concrete  is  made  of  cement,  sand,  gravel, 
and  broken  stone,  the  gravel  being  intermediate  in  size 
between  the  sand  and  the  broken  stone.  Good  dense  con- 
crete may  be  made  of  this  combination,  if  suitable  propor- 
tions are  determined. 

Concrete  is  sometimes  made  of  sand  and  cement  only, 
there  being  a  large  quantity  of  sand  in  proportion  to  the 
cement,  say  I  of  cement  to  7  or  8  of  sand.  This  does  not 
make  good  concrete.  The  voids  in  the  sand  cannot  be  filled 
by  so  small  a  proportion  of  cement. 

Concrete  may  be  mixed  by  hand  or  by  machinery. 
When  hand  mixed  the  following  is  probably  the  most  ap- 
proved method.  First  the  sand  is  dumped  on  the  mixing 
board  and  spread  out  to  a  thickness  of  about  three  inches. 
Over  this  the  cement  is  dumped  and  spread  out  evenly. 
This  dry  sand  and  cement  is  then  turned  over  with  shovels 
two  or  three  times,  and  the  pile  is  leveled  off.  On  this 
the  broken  stone  or  gravel,  previously  wetted,  is  dumped 
and  spread  out  evenly  so  as  to  cover  the  sand  and  ce- 
ment. The  full  amount  of  water  is  then  measured  and 
poured  on.  As  only  the  aggregate  is  exposed,  the  water 
may  be  poured  or  dashed  on  without  particular  care,  since 
the  danger  of  washing  out  the  cement  is  removed.  The 
whole  should  now  be  turned  over  with  shovels  two  or 
three  times. 

When  concrete  is  mixed  by  machinery,  all  of  the  in- 
gredients, including  the  water,  are  carefully  measured  and 
placed  in  the  mixer.  For  mixtures  in  which  little  water 
is  to  be  used  it  may  be  necessary*  in  order  to  get  a  uni- 
form mixture,  to  mix  the  dry  ingredients  without  any 
water  first  and  then  add  the  water  and  continue  the  mix- 
ing until  this  is  incorporated  in  the  mass.  The  number 
of  turns  of  the  mixer,  or  the  time  required  to  effect  an 
intimate  and  thorough  mixture  will  depend  somewhat 
upon  the  kind  of  mixer.  This  can  be  well  judged  by  the 

60 


uniformity  of  the  product  in  color  and  by  inspection  to  see 
if  the  grains  of  sand  and  the  stones  are  covered  with  ce- 
ment. The  whole  mass  should  have  the  color  of  the  ce- 
ment. Concrete  not  well  mixed  will  have  patches  of  bare 
sand  and  stones.  Regularity  both  in  the  proportion  of 
the  ingredients  and  in  the  amount  of  mixing  are  very  im- 
portant in  any  concrete  work  and  are  of  special  moment 
in  reinforced  concrete  as  well  as  any  work  that  is  to  be 
watertight.  When  the  time  of  mixing  required  to  give  a 
thorough  mixture  is  ascertained,  this  length  of  time  should 
be  allowed  for  each  batch. 

Usually  about  10  or  15  turns  of  the  mixer  are  required 
to  give  a  thorough  mixture.  The  time  required  is  from  I 
to  iVz  minutes.  It  requires  about  two  to  three  minutes 
per  batch  to  put  in  the  materials  and  take  out  the  con- 
crete, if  the  handling  of  materials  can  be  expeditiously 
done. 

Lean  mixtures  require  more  mixing  than  rich  ones,  be- 
cause it  is  more  difficult  to  distribute  the  smaller  amount 
of  cement  thoroughly  through  the  mass.  Dry  mixtures 
require  more  mixing  than  wet  ones. 

It  is  well  to  mold  a  small  cube  of  concrete  from  the 
batch  occasionally.  These  cubes  will  be  useful  in  gaging 
the  kind  of  concrete  turned  out,  and  by  the  time  required 
for  them  to  set  the  hardness  of  the  work  may  be  judged. 
When  concrete  is  placed  in  unusual  conditions  such  a  sam- 
ple placed  in  the  same  conditions  and  accessible  for  in- 
spection furnishes  an  index  to  the  character  of  the  placed 
concrete. 

Concrete  should  not  be  too  wet  or  too  dry.  If  too  wet 
it  will  shrink  an  excessive  amount  from  drying  out;  if 
too  dry  when  placed,  it  will  not  be  dense,  as  the  mortar 
will  not  run  into  the  spaces.  Formerly,  when  mass  con- 
crete was  about  all  the  kind  made,  very  dry  concrete  was 
generally  specified,  just  enough  water  being  used  to  satisfy 
the  needs  of  the  cement  in  setting;  and  this  was  heavily 
rammed.  This  is  not  very  objectionable  in  mass  concrete, 
and  it  has  some  advantages.  One  of  these  is  that  the  drier 

61 


concrete  will  attain  its  strength  sooner  than  wet  concrete. 
Wet  concrete  is  generally  considered  to  be  best  for  al- 
most all  purposes,  though  the  amount  of  water  which 
should  be  used  is  not  the  same  in  all  cases. 

The  chief  advantage  in  dry  concrete  is  its  faculty  of 
setting  up  in  a  shorter  time  than  wet  concrete.  When 
a  piece  of  construction  is  to  receive  its  load  soon  after 
placing  the  concrete,  it  is  best  to  use  a  dry  mixture,  if  the 
conditions  are  not  such  as  to  render  such  a  mixture  harm- 
ful for  other  reasons.  Some  concrete  block  manufacturers 
take  advantage,  in  making  their  blocks,  of  the  fact  that 
dry  mixtures  hold  up  in  a  short  time  better  than  wet  ones. 
They  use  a  mixture  that  is  simply  moist,  so  that  blocks 
can  be  removed  from  the  molds  about  as  soon  as  they 
are  molded.  The  result  is  that  the  blocks  are  spongy,  and 
we  see  houses  built  of  the  blocks  turn  dark  gray  in  a 
rain  because  of  the  absorption  of  water.  Such  use  of 
dry  concrete  can  only  serve  to  discredit  concrete  itself. 

Another  advantage  in  dry  concrete  is  that  it  is  less  lia- 
ble to  freeze  in  cold  weather  than  wet  concrete.  It  should 
be  borne  in  mind  that  much  water  in  concrete  in  cold 
weather  renders  it  more  liable  to  the  action  of  frost. 
However,  other  means  of  preventing  freezing  should  be 
employed  rather  than  the  use  of  concrete  that  is  too 
dry  for  the  purpose  intended.  On  the  other  hand  in  very 
warm  weather  an  excess  of  water  is  advantageous,  be- 
cause it  prevents  the  concrete  from  too  rapid  drying  out 
due  to  the  heat. 

Dry  or  mealy  concrete  has  many  disadvantages.  It  is 
unfit  to  use  in  walls  that  are  to  keep  out  moisture.  A 
mealy  concrete  wall  allows  water  to  flow  through  it  very 
freely.  It  is  unfit  to  use  in  clycopean  or  rubble  concrete, 
because  it  will  not  flow  around  the  large  stones  and  coat 
them  with  cement.  For  similar  reasons  it  is  totally  un- 
fit for  use  in  reinforced  concrete  work,  as  it  will  not  flow 
around  the  steel  and  coat  it  with  cement.  Because  dry 
concrete  is  porous  there  will  be  voids  around  the  rein- 
forcing steel  as  well  as  in  the  other  parts.  The  steel  is 


thus  deprived  of  the  protection  which  the  concrete  must 
afford,  if  the  combination  is  to  be  lasting.  Concrete  must 
be  wet  to  pack  around  the  reinforcing  steel  or  embedded 
stones  and  to  cover  them  with  cement.  Both  of  these 
requisites  are  of  prime  importance  in  reinforced  concrete. 
Steel  rods  will  not  be  gripped  as  firmly  in  a  porous  con- 
crete as  in  a  dense  concrete.  Dry  concrete  lacks  cohe- 
sion, and  the  cohesion  of  concrete  has  much  to  do  with 
the  gripping  of  the  steel.  It  is  of  special  importance  in 
cinder  concrete,  reinforced,  that  a  wet  concrete  be  used, 
so  that  the  cement  will  coat  the  steel  and  protect  it  from 
sulphur  or  other  harmful  agents  in  the  cinders. 

Dry  concrete  requires  tamping;  the  drier  the  concrete, 
generally,  the  heavier  the  tamping  necessary.  Dry  concrete 
for  this  further  reason  is  unsuitable  in  reinforced  concrete 
work.  Tamping  around  reinforcing  steel  is  apt  to  displace 
the  steel  as  well  as  to  disturb  or  spring  the  forms.  The 
concrete  around  the  reinforcement  should  be  worked  into 
the  spaces  by  puddling  rather  than  by  tamping,  and  the 
consistency  of  the  mixture  should  be  such  as  to  admit  of 
this  operation.  As  near  a  liquid  as  possible  is  evident- 
ly the  best  consistency  to  effect  this  end,  but  other  con- 
siderations must  be  taken  into  account.  If  concrete  is 
too  wet  it  will  shrink  an  excessive  amount  on  setting  and 
drying.  This  may  give  rise  to  shrinkage  cracks  or  other 
trouble  that  such  change  of  volume  would  naturally  lead 
to. 

With  concrete  too  wet,  unless  the  forms  are  very  close, 
approximating  water-tightness,  liquid  mortar  will  be 
wasted  through  the  crevices.  This  is  a  fault  sometimes 
met  with  in  concrete  work,  namely,  the  mortar  being  of 
too  watery  a  consistency,  or  the  forms  lacking  the  proper 
tightness,  not  only  results  in  a  waste  of  mortar  but  leaves 
the  concrete  spongy,  where  the  mortar  has  leaked  out. 
This  may  give  the  appearance  of  dry  concrete,  whereas 
the  cause  is  just  the  opposite. 

Another  danger  that  may  attend  the  use  of  sloppy  con- 
crete is  the  formation  of  laitance.  This  is  a  milky  or 

63 


slimy  substance  that  sometimes  gathers  in  the  excess 
water  on  the  surface  of  concrete.  It  is  composed  of  about 
the  same  ingredients  as  the  cement,  but  it  does  not  hard- 
en as  the  cement,  remaining  rather  in  a  gellatinous  state. 
Besides  taking  from  the  cement  useful  elements  needed  in 
the  concrete,  the  laitance,  if  not  removed,  leaves  a  film 
in  the  concrete  where  it  is  not  bonded  together  as  it  should 
be. 

For  reinforced  concrete  work  there  must  tie  found  a 
mean  between  too  wet  a  concrete  and  too  dry  a  concrete 
that  will  meet  the  conditions.  The  proper  mean  is  not  a 
mixture  medium  in  constancy,  but  a  very  wet  mixture. 
The  concrete  should  assume  a  nearly  level  surface.  It 
should  flow  sluggishly  around  the  reinforcing  steel  and 
require  little  or  no  tamping.  A  little  shrinking  in  rein- 
forced concrete  is  an  aid  rather  than  a  detriment,  because 
the  shrinking  of  concrete  acts  to  grip  the  steel. 

Other  works  than  reinforced  concrete  do  not  generally 
require  such  wet  mixtures.  Work  that  is  to  be  water- 
proof or  nearly  so  should  be  made  of  a  wet  mixture  and 
should  be  puddled,  as  in  the  case  of  reinforced  concrete, 
to  work  out  air  bubbles  and  to  solidify  the  mass. 

There  should  not  be  an  excess  of  water  in  the  con- 
crete base  for  a  sidewalk,  where  a  richer  mortar  finish  is 
to  be  put  on  subsequently.  Tamping  will  bring  this  water, 
and  probably  accompanying  laitance,  to  the  surface  awd 
the  finish  coat  will  not  bond  well  to  it.  Pavers  usually  em- 
ploy a  rather  dry  mixture  for  the  base  and  tamp  it  well. 
However  it  is  believed  that  a  better  pavement  would  re- 
sult from  the  use  of  a  wet  mixture  and  little  tamping, 
with  the  finish  coat  floated  in  at  the  same  time  and  with 
as  little  troweling  as  possible. 

Wet  mixtures  do  not  require  as  much  mixing  to  distrib- 
ute the  cement  through  the  mass  as  dry  ones.  However 
the  liquid  state  of  the  concrete  may  make  an  insufficient 
amount  of  mixing  appear  to  be  enough;  so  that  just  as 
much  vigilance  is  required  to  insure  the  proper  mixing. 


Dry  mixtures  are  more  liable  than  wet  ones  to  ball  in 
the  mixer,  that  is,  to  gather  in  lumps,  as  the  materials 
will  not  flow  well  without  the  lubricating  water.  With  no 
water  whatever  in  the  mixer  there  would  be  no  cohesion 
and  the  materials  would  mix,  whereas  a  little  water  would 
give  a  cohesion  that  may  result  in  the  balling  referred  to. 
It  may  be  necessary  in  some  cases  to  mix  the  materials 
dry  and  then  add  the  water  giving  the  mixer  a  few  more 
turns.  While  hand  mixing  in  general  is  less  satisfactory 
than  machine  mixing,  it  is  possible  that  in  some  cases  for 
very  dry  mixtures  hand  mixing  will  produce  a  better  con- 
crete. 

As  to  the  strength  attained  by  wet  and  dry  mixtures, 
it  is  found  that  given  a  number  of  samples  of  different 
consistency  the  drier  mixtures  will  at  first  show  greater 
strength.  After  a  few  days  the  mixtures  having  more 
water  will  attain  the  strength  of  the  drier  ones  and  be- 
gin to  surpass  them.  In  general  the  more  water  used  in 
the  mixture  the  longer  it  will  be  in  attaining  its  full 
strength.  Medium  and  wet  mixtures,  after  many  months, 
reach  about  the  same  strength.  Very  wet  and  very  dry 
mixtures  are  both  weaker  on  long  time  tests  than  those 
in  which  the  consistency  is  not  excessive. 

The  amount  of  water  required  in  concrete  depends  upon 
the  porosity  of  the  aggregate,  the  proportion  of  the  in- 
gredients, the  wetness  of  the  sand  and  aggregate  before 
being  brought  together,  the  fineness  of  the  sand,  (fine 
sand  requires  more  water  than  coarse  sand.)  and  to  some 
extent  on  the  brand  of  cement.  If  the  sand  and  stone: 
were  thoroughly  wet  before  mixing,  the  amount  of  water 
would  depend  largely  on  the  amount  of  cement  in  a  batch, 
as  moistening  of  these  will  lessen  the  amount  of  water 
required  to  be  placed  in  the  mixer. 

Dry  concrete  is  usually  understood  to  be  of  the  con- 
sistency of  moist  earth.  It  will  retain  its  shape  wrhen 
squeezed  in  the  hand.  No  water  will  flush  to  the  surface 
on  tamping. 

65 


Medium  concrete  is  of  such  consistency  that  it  will  not 
quake  in  handling  and  will  not  quake  under  light  tamp- 
ing. When  well  or  heavily  tamped,  the  concrete  will  quake 
and  water  will  flush  to  the  surface. 

Wet  concrete  will  quake  in  handling  and  cannot  be 
tamped  very  much. 

In  ordinary  concrete  mixtures  dry  concrete  will  require 
about  5  to  6  per  cent,  of  water  (based  on  total  weight  of 
dry  materials),  medium  concrete  will  require  about  6  to  8 
per  cent,  of  water,  and  wet  concrete  will  require  about 
8  to  10  per  cent.  This  is  an  average  of  about  i,  i^,  and 
i%  gallons  per  cubic  foot  of  concrete  for  the  three  re- 
spective grades.  Per  bag  of  cement  it  takes  about  3  to  4 
gallons  of  water  for  dry  concrete,  4  to  6  for  medium,  and 
6  to  8  for  wet.  The  amount  of  water  should  not  be 
specified  in  any  case,  unless  the  proper  consistency  and  the 
amount  of  water  required  therefor  have  been  previously 
determined  by  trial  with  the  materials  to  be  used.  Some 
materials  will  require  amounts  of  water  differing  consid- 
erably from  the  foregoing. 

It  is  important  to  wet  the  aggregate  before  it  is  mixed 
with  the  other  ingredients  especially  in  the  drier  mix- 
tures and  in  hand  mixed  work,  and  particularly  when  the 
aggregate  is  porous  or  absorbent.  This  wetting  of  the 
aggregate  in  the  pile  allows  it  time  to  absorb  water  that 
might  otherwise  be  robbed  from  the  cement  of  the  con- 
crete, if  the  stone  is  not  wet  previous  to  the  mixing. 

The  following  table  gives  approximately  the  amounts 
of  materials  of  average  quality  required  to  make  one 
cubic  yard  of  concrete  of  the  three  most  common  mix- 
tures. 

Proportion  Bbl.,  P.  Cement    Cu.  Ft.  Sand    Cu.  Ft.  Stone 
1:2:4  1.44  11.5  23.0 

1:3:6  1.04  12.5  25.0 

i  :4 :8  .78  12.5  25.0 

The  measuring  of  the  ingredients  of  concrete  is  not  very 
satisfactorily  done  on  the  average  job.  This  is  because 
of  uncertainty  as  to  the  capacity  of  a  wheelbarrow,  the 


commonly  used  means  of  carrying  the  sand  and  stone  to 
the  mixer.  An  average  wheelbarrow  contains  from  2  to 
3%  cu.  ft.,  depending  on  the  amount  it  is  heaped.  One 
method  of  proceedure  is  to  make  a  box  just  one  foot  each 
way,  inside  dimensions,  and  fill  this  twice  with  the  bro- 
ken stone  and  dump  it  into  the  wheelbarrow.  By  observ- 
ing the  amount  it  is  heaped  each  wheelbarrow  load  can  be 
heaped  (or  struck  off)  to  the  same  extent.  The  same  is 
done  with  the  sand,  so  that  the  appearance  of  two  cubic 
feet  of  sand  may  also  be  noted.  Then  two  bags  of  ce- 
ment are  called  one  part,  or  two  cubic  feet,  and  each 
wheelbarrow  of  sand  or  stone  is  called  one  part.  For 
hand  mixing  of  a  1 13 :6  mixture  there  would  be  used  2 
bags  of  cement,  3  wheelbarrows  of  sand  and  6  of  stone 
or  gravel.  Four  to  six  men  with  shovels  would  be  needed 
to  turn  this  over.  A  half  yard  batch  mixer  could  take  in 
the  same  quantities. 

This  way  of  measuring  in  wheelbarrows  is  not  very  ac- 
curate and  not  very  satisfactory  on  any  but  mass  work,  un- 
less the  loading  of  the  wheelbarrows  is  carefully  watched. 
If  there  is  an  incline  from  the  stone  and  sand  piles  to  the 
mixer,  the  men  are  less  apt  to  overload  their  wheelbar- 
rows, as  two  cubic  feet  is  about  all  they  will  care  to  push 
up  the  grade. 

A  more  satisfactory  and  more  accurate  method  of  meas- 
uring the  ingredients  consists  in  the  use  of  a  bottomless 
box  having  handles  projecting  from  the  ends.  Such  a 
box  made  of  the  proper  size  to  contain  a  unit  quantity, 
for  a  batch  of  concrete,  can  be  laid  on  the  mixing  board 
and  filled  level  full  of  sand  once  and  of  stone  twice  (or 
two  boxes  could  be  used  where  the  volume  of  stone  is  not 
double  that  of  sand.)  This  serves  to  measure  the  mater- 
ials accurately,  but  it  requires  more  handling  to  dispose 
them,  after  this  measuring,  in  an  advantageous  position 
for  mixing.  This  adds  to  the  expense  of  mixing  the  con- 
crete. 

One  method  of  using  the  bottomless  boxes  mentioned 
in  the  last  paragraph  is  to  measure  the  sand  first  in  such 

t>7 


a  box  and  then  spread  it  over  the  board  and  mix  in  the 
cement  dry.  After  this  mixing  the  surface  is  leveled  off 
and  the  box  placed  upon  it  and  filled  with  the  stone.  Thei 
the  stone  is  spread  over  the  mixed  sand  and  cement  to 
cover  it  and  the  water  thrown  on  and  the  final  mixing 
done.  The  sides  of  the  boxes  should  not  be  high.  A 
wheelbarrow  could  not  be  dumped  over  the  sides  of  a  high 
box,  and  a  flat  box  would  not  necessitate  as  much  spread- 
ing of  the  materials  after  the  box  is  lifted  as  a  high  box. 
The  bottomless  box  method  of  measuring  the  materials 
cannot  be  used  in  this  same  way  in  batch  mechanical  mix- 
ers; a  dumping  square  box,  however,  could  be  rigged  up 
from  which  to  load  wheelbarrows,  and  exact  measurement 
could  be  effected  in  this  way. 

There  are  other  ways  in  which  the  problem  of  measur- 
ing the  materials  is  solved.  The  chief  points  of  the  prob- 
lem are  to  effect  the  maximum  accuracy  of  measurement 
with  the  minimum  amount  of  handling.  It  is  desirable  to 
avoid  high  lifts  of  the  sand  and  stone,  either  in  the  shovel 
or  in  the  wheelbarrow.  It  is  also  desirable  to  accomplish 
these  preliminaries  to  the  mixing  in  the  shortest  time 
possible. 

The  measuring  of  the  cement  is  fortunately  greatly  sim- 
plified on  account  of  the  way  in  which  standard  cements 
are  packed.  A  barrel  of  Portland  cement  of  the  stand- 
ard size  weighs  375  Ibs.  and  contains,  when  well  com- 
pacted, about  3.8  cu.  ft.  When  put  in  a  measure  and  well 
shaken,  this  quantity  will  occupy  just  about  4  cu.  ft. 
Hence  a  standard  barrel  can  be  taken  as  four  cubic  feet. 
Cement  usually  comes  in  bags,  four  of  these  being  a  bar- 
rel of  cement.  A  bag  of  cement  can  then  be  taken  as  a 
cubic  foot.  It  is  important,  however,  to  measure  and 
weigh  some  sample  bags  of  the  cement  used  on  any  work 
to  see  that  they  contain  a  cubic  foot  and  weigh  close  to 
94  Ibs.  each.  If  the  bags  are  found  not  to  contain  a  full 
cubic  foot,  the  other  measures  should  be  made  on  the 
basis  of  the  actual  volume  of  cement  in  a  bag, 

68 


A  bag  of  cement  will  sometimes  contain  lumps.  These 
should  be  broken  up,  or,  if  they  are  too  refractory,  they 
should  be  thrown  out  and  good  cement  used  to  make  up 
the  deficiency. 

A  pile  of  stone  in  cold  weather  may  sometimes  contain 
lumps  of  ice.  These  should  be  watched  for  and  eliminat- 
ed. 

It  is  very  important  to  have  an  inspector  to  watch  the 
mixing  of  concrete.  He  should  count  the  bags  of  ce- 
ment; keep  tab  on  the  amounts  of  materials;  see  that  the 
mixer  runs  long  enough;  see  that  the  consistency  and 
fluidity  is  right;  see  that  no  blocks  of  wood,  lumps  of 
mud  or  clay,  paper  from  sacks,  ice,  lumps  of  hard  ce- 
ment, etc.  go  through;  see  that  lumps  of  hard  cement  are 
compensated  for  with  good  cement;  see  that  the  concrete 
is  well  mixed,  that  it  is  uniform,  that  it  has  not  balled  in 
the  mixer,  etc. ;  see  that  the  mixer  is  clean  before  start- 
ing; see  that  the  materials  are  running  uniform,  regular  in 
size  and  not  mixed  with  dirt,  no  single  wheelbarrows  com- 
posed entirely  of  large  stones  or  of  small  stones,  etc. 

Materials  should  be  moved  by  power  wherever  practi- 
cable. They  should  be  stored  high  where  possible.  If 
raised  to  bins  when  delivered  on  the  job,  they  may  be 
drawn  out  with  use  of  little  labor.  This  storing  of  the 
materials  may  often  be  done  by  use  of  cranes.  It  is 
better  to  handle  the  materials  in  this  way  than  to  dump 
them  on  the  ground  and  shovel  them  up.  They  will  be 
cleaner,  and  the  stone  is  less  liable  to  run  irregular. 

One  method  of  raising  materials  to  the  mixer  is  to  use 
an  incline  with  a  gravity  dumping  car  to  material  pile. 
This  is  drawn  up  to  the  mixer  by  cable  from  the  mixer 
engine  or  other  power  and  allowed  to  return  by  its  own 
weight 


Steel  for  Reinforced  Concrete. 

Steel  for  reinforced  concrete  should  preferably  be  open 
hearth  steel,  though  Bessemer  steel  may  safely  be  used  for 
rods  and  for  plates  and  shapes  that  are  punched  if  the 
punched  holes  are  reamed. 

The  ultimate  strength  of  the  steel  is  not  a  matter  of 
much  importance,  neither  is  the  elastic  limit,  except  as 
these  properties  indicate  uniformity  in  the  product.  It 
should  be  a  good  grade  of  soft  steel.  It  is  of  more  import- 
ance that  it  stand  the  bend  test  of  soft  steel  than  that  its 
ultimate  strength  and  elastic  limit  be  high.  The  reason 
why  high  elastic  limit  and  high  ultimate  strength  are  not 
essential  characteristics  of  steel  embedded  in  concrete  is 
the  simple  fact  that  these  qualities  cannot  be  made  use 
of  in  proper  design  of  reinforced  concrete.  This  is  di- 
rectly contrary  to  a  great  amount  of  trade  literature  and 
some  technical  literature.  Commercial  soft  steel  is  almost 
universally  of  an  ultimate  tensile  strength  of  from  50,000 
to  60,000  Ibs.  per  sq.  in.  and  a  strength  at  elastic  limit  of 
30,000  to  40,000  Ibs.  per  sq.  in.  This  latter  is  about  three 
times  the  safe  value  that  ought  to  be  allowed  on  the  steel, 
because  above  this  value  cracks  begin  to  appear,  and  there 
can  be  no  justification  for  a  design  that  anticipates  cracked 
beams  and  slabs.  There  is  therefore  ample  margin  of 
safety  in  any  good  soft  steel. 

If  high  steels  showed  smaller  elongations  for  a  given 
unit  stress  (for  stress  within  the  elastic  limit)  than  soft 
steels,  there  would  be  some  justification  for  their  use,  as 
they  would  then  not  stretch  out  as  much  under  a  given 
stress,  and  the  concrete  would  be  less  liable  to  be  cracked. 
But  the  modulus  of  elasticity  is  one  property  that  is  prac- 
tically constant  for  all  grades  of  steel.  Even  soft  wrought 
iron  has  a  modulus  of  elasticity  almost  as  great  as  the 
hardest  steel.  The  simplest  conception  of  the  modulus  of 
elasticity,  designated  as  E,  is  a  unit  stress  that  would 
stretch  a  piece  of  steel  out  to  double  its  original  length, 
at  the  rate  at  which  it  stretches  within  the  elastic  limit. 

70 


The  modulus  of  elasticity  of  steel  is  about  30,000,000,  if 
then  a  piece  of  steel  is  stressed  to  10,000  Ibs.  per  sq.  in., 
it  will  stretch  one-three-thousandth  of  its  length.  Beyond 
the  elastic  limit  different  grades  of  steel  exhibit  different 
characteristics.  Soft  steels  stretch  out  more  before  fail- 
ure, while  high  steels  and  soft  steels  that  have  been  rolled 
or  drawn  cold  or  twisted  cold,  break  without  much 
stretch  or  reduction  of  area  at  point  of  fracture.  This 
lack  of  stretch  beyond  the  elastic  limit  is  held  out  as  a  ben- 
efit in  trade  literature.  It  is  a  positive  detriment.  If  fail- 
ure occurs  in  steel  that  will  not  stretch,  it  will  be  sudden 
and  without  warning,  whereas  if  the  steel  stretches  out, 
it  will  allow  a  beam  or  slab  to  sag  before  failure.  Be- 
sides giving  warning  of  failure  the  sagging  will  in  many 
cases  reduce  the  stress  in  the  steel  very  materially.  The 
author  has  seen  tests  of  slabs  reinforced  with  soft  steel 
that  sagged  enormously  and  could  not  be  broken. 

The  reason  why  it  is  important  that  steel  stand  the  cold 
bend  test  is  because  rods  are  very  often  curved  and  bent 
in  construction.  This  bending  should  be  done  cold,  for  if 
the  steel  is  heated,  its  internal  structure  is  changed,  and 
annealing  would  be  necessary  to  restore  it.  Soft  steel  of 
ordinary  manufacture  will,  in  general,  stand  more  punish- 
ment than  harder  grades  of  steel.  The  threading  of  rods 
and  punching  of  plates  or  shapes  are  less  liable  to  cause 
incipient  cracks  or  hardened  metal  in  soft  steel  than  in 
high  steel.  These  are  also  processes  to  which  the  embed- 
ded steel  may  be  subjected. 

Special  steel,  while  it  has  a  high  sound,  does  not  possess 
any  needful  characteristics,  as  an  element  in  reinforced 
concrete,  that  are  not  possessed  by  the  cheap  commer- 
cial article.  This  is  true  because  of  the  limitations  of  the 
concrete.  Good  soft  steel  is  not  a  special  steel  but  is  the 
commonest  product  of  the  steel  furnace.  It  is  important, 
however,  that  it  be  good  and  that  it  be  soft,  that  is,  not  a 
high  carbon  steel. 

There  should  be  a  wide  margin  of  safety  in  the  amount 
that  a  steel  rod  will  bend.  A  piece  of  steel  of  high  ulti- 

71 


mate  strength  may  stand  a  bend  of  100  degrees  and  fail 
if  bent  105  degrees.  It  is  clear  that  this  steel  would  not 
be  fit  to  use  where  it  is  bent  at  an  angle  anywhere  near 
approaching  this. 

The  best  carbon  steel  for  structural  purposes  is  found 
to  possess  an  ultimate  strength  between  55,000  and  65,000 
Ibs.  per  sq.  in.  Formerly  two  grades  of  steel  were  rec- 
ognized in  most  specifications  for  structural  steel  work 
with  allowed  limits  that  overlapped  two  or  three  thousand 
pounds  around  the  60,000  mark.  The  result  was  that 
manufacturers  usually  succeeded  in  making  nearly  all  of 
their  structural  steel  within  the  overlap,  so  that  it  would 
fill  either  specification,  though  a  wide  difference  in  allowed 
unit  stresses  was  sometimes  permitted.  The  allowed  lim- 
its given  at  the  beginning  of  this  paragraph  represent  a 
steel  that  is  a  mean  between  the  older  grades  of  soft  and 
medium  steel.  It  is  also  about  midway  in  tensile  strength 
between  the  very  soft  steel  now  used  for  rivets  and  the 
higher  steel  used  for  eyebars  and  other  forgings.  It  has 
been  found  by  experience  to  be  satisfactory  for  structural 
purposes.  For  reinforced  concrete  it  satisfies  every  struc- 
tural requirement,  and  because  of  its  availability  it  is  the 
most  economical  material  that  can  be  used. 

Tests  made  to  see  that  the  ultimate  strength  lies  between 
these  limits  are  very  useful  to  ascertain  that  the  steel  is 
regular  in  quality.  Dead  soft  steels  may  be  ruined  in  the 
manufacture.  High  steels  will  not  stand  bending. 

The  elastic  limit  of  the  steel  should  be  not  less  than  one- 
half  of  the  ultimate  strength  and  the  stretch  in  a  measured 
length  of  8  inches  should  be  not  less  than  24  per  cent.  It 
should  stand  the  cold  and  quench  bend  test,  180  degrees 
flat,  without  fracture.  In  the  quench  bend  test  steel  is 
heated  to  a  cherry  red,  as  seen  in  the  dark,  and  quenched 
in  water  at  ordinary  temperature,  before  bending. 

The  proper  use  of  steel  in  concrete  is  in  small  sections 
well  distributed  throughout  the  mass.  The  bars  should  be 
separated  from  each  other  to  give  the  gripping  effect  of 
the  concrete  full  play.  If  they  are  placed  in  a  layer  close 


together,  a  cleavage  joint  is  formed  and  the  concrete  is 
liable  to  break  off.  This  would  be  the  case  in  a  close  coil 
or  set  of  rings  close  together  or  in  a  set  of  rods  lying 
close  together  near  the  bottom  of  a  beam.  Plates  or 
sheets  of  steel  should  not  be  used  as  separators  or  spacers 
for  rods,  as  these  will  also  form  cleavage  planes.  If  heavy 
rods  are  used,  surrounded  by  comparatively  little  concrete, 
the  concrete  is  unable  to  grip  the  steel  and  the  differen- 
tial expansion  due  to  change  in  temperature  will  crack  the 
concrete.  Pvramids  of  concrete  surrounding  the  bases  of 
out-door  steel  columns  seldom  last  through  a  winter  with- 
out being  cracked.  Girders  covered  with  a  shell  of  con- 
crete would  be  subject  to  the  same  detrimental  effect  of 
differential  expansion. 

The  steel  should  not  be  placed  close  to  the  surface  of 
the  concrete.  It  cannot  be  gripped  properly  unless  it  is 
deep  enough  in  the  concrete  for  the  latter  to  take  hold. 
It  cannot  be  protected  from  rust  and  fire  unless  there  is 
some  concrete  between  the  steel  and  these  destroying  ele- 
ments. It  is  bad  practice  to  lay  the  steel  on  the  forms 
and  then  the  concrete  on  this.  The  steel  is  neither  properly 
protected  nor  gripped  by  such  means.  The  depth  to  which 
steel  should  be  buried  depends  upon  the  size  of  the  sec- 
tion. It  is  manifest  that  the  heavier  the  section  tlie  more 
concrete  is  needed  to  grip  it  and  to  overcome  differential 
expansion.  If  rods  are  bedded  deeper  they  will  be  less 
affected  by  external  change  of  temperature.  Heavy  rods 
are  of  more  importance  in  a  structure,  hence  their  protec- 
tion is  of  more  vital  importance  than  that  of  light  rods. 

Standard  sizes  of  rods  or  shapes  should  be  used  as 
much  as  possible,  so  that  they  can  be  obtained  without 
delay  from  the  mills.  Also  as  few  different  sizes  as  pos- 
sible should  be  employed.  Simple  details  are  essential. 
A  complex  structure  will  be  difficult  to  surround  properly 
with  concrete.  There  should  be  no  broad  flat  surfaces  to 
work  the  concrete  under. 

The  steel  work  should  be  designed  with  a  view  of  its 
being  easily  placed  in  proper  position  and  held  there 

73 


against  the  displacing  tendencies  due  to  the  placing  of  the 
concrete.  Where  rods  cross,  they  should  be  wired  to- 
gether, and  this  should  be  done  before  the  forms  are 
erected  to  the  point  that  they  will  interfere  by  preventing 
free  access  to  the  rods.  Extra  wires  may  often  be  used 
to  advantage  to  tie  the  rods  in  place.  These  wires  may 
serve  the  further  purpose  of  holding  the  sides  of  the  forms 
from  spreading.  They  can  be  cut  off  at  the  surface  when 
the  forms  are  removed. 

Rods  in  the  bottom  of  a  slab  can  be  kept  from  lying  on 
the  bottom  of  the  form  by  placing  small  stones  under  them 
just  before  the  concrete  is  placed. 

There  is  nothing  better  than  round  rods  for  reinforced 
concrete  for  the  reason  that  positive  end  anchorages  can 
be  made  by  means  of  nuts  and  washers,  or  large  square 
plates  having  threaded  holes,  and  because  splices  can  be 
made  by  means  of  sleeve  nuts.  Both  the  anchorage  and 
the  splice  will  take  nearly  as  much  stress  as  the  full  sec- 
tion of  the  rod.  No  other  kind  of  anchorage  or  splice  has 
the  same  efficiency.  The  thread  and  nut  detail  comes  into 
play  immediately  without  any  slip.  Rods  laid  together 
and  bound  would  have  to  slip  before  receiving  much  stress. 
End  hooks  and  curves  are  no  doubt  of  some  aid  as  a 
precautionary  measure ;  they  may  show  strength,  after  par- 
tial straightening  of  the  rod,  before  ultimate  failure.  A 
hook  cannot  be  seriously  considered  as  an  efficient  end  an- 
chorage for  a  rod  taking  practically  its  full  strength  near 
the  end. 

Wire  cables  in  concrete  are  faulty  from  every  standpoint 
considered.  The  stretch  in  a  wire  cable,  as  compared 
with  a  solid  steel  rod,  as  shown  by  tests  made  at  Water- 
town  Arsenal  in  1896  may  be  as  much  as  four  times  that 
of  the  plain  steel  rod  under  the  same  unit  stress.  The 
safe  unit  allowed  on  wire  cables  (to  be  economical)  would 
be  about  four  times  as  much  as  that  on  plain  steel.  Hence 
the  stretch  in  the  steel  cable  may  be  sixteen  times  as  much 
as  in  the  plain  rod  when  consistent  unit  stresses  are  em- 
ployed. The  placing  of  initial  tension  in  the  cable  can 

74 


scarcely  do  more  than  take  out  the  curving  tendency  due 
to  the  winding  of  the  coil.  A  stress  of  any  magnitude  on 
the  cable  could  scarcely  be  resisted  by  the  supporting  walls 
or  beams. 

Sharp  bends  should  not  be  made  in  steel  rods  under 
stress,  as  the  concrete  cannot  resist  the  stress  at  the 
knuckle.  Curves  with  a  radius  20  times  the  diameter  of 
rod  are  permissible. 

No  welds  should  be  allowed  where  the  steel  is  under 
stress  approaching  that  allowed  on  the  full  section.  If 
rods  were  found  to  be  a  little  too  short  to  reach  between 
supports,  it  would  not  be  harmful  to  weld  a  short  piece  on. 
In  general  all  welds  in  steel  should  be  avoided. 

Steel  that  is  to  be  placed  in  concrete  should  be  free  from 
scale  and  thick  rust.  A  thin  coat  of  rust  is  not  objection- 
able. It  is  well  to  let  new  rods  rust  so  as  to  loosen  the 
mill  scale.  The  scale  should  then  be  scraped  off  or  brushed 
off  with  wire  brushes.  The  coating  of  steel  with  grout 
to  preserve  it  from  rust  is  a  doubtful  expedient.  The  thin 
layer  of  cement  dries  out  and  does  not  set  properly.  It 
may  not  bond  with  the  cement  of  the  concrete.  It  is  bet- 
ter to  have  the  fresh  concrete  come  in  contact  with  the 
steel.  A  more  intimate  union  is  effected. 

No  paint  should  be  used  on  any  steel  embedded  in  con- 
crete. Grease  and  dirt  are  objectionable  and  should  be 
removed  before  the  steel  is  placed. 

Steel  should  be  placed  well  in  advance  of  the  concrete, 
so  that  any  delay  in  placing  it  will  not  hold  up  the  plac- 
ing of  the  concrete. 

Vertical  reinforcement  in  hooped  columns  should  be  of 
smooth  rods  so  that  when  the  concrete  shrinks  in  setting 
it  will  not  be  prevented  from  settling  down. 

No  reliance  should  be  placed  on  a  short  length  of  a  rod 
cither  plain  or  deformed  to  act  as  anchorage.  Where  two 
thin  walls  intersect  they  should  be  reinforced  with  steel. 
If  there  is  no  special  stress  acting  on  the  walls  it  is 
enough  to  curve  or  bend  rods  around  the  corner.  If, 
however,  there  is  pressure  on  the  walls,  as  in  the  case  of 

75 


the  walls  of  a  rectangular  cistern  or  the  analogous  case 
of  the  bottom  slab  and  rib  or  counterfort  in  a  retaining 
wall,  the  bend  in  the  rods  would  be  too  sharp  to  be  effec- 
tive. In  such  case  a  short  length  even  of  a  deformed  rod 
is  entirely  inadequate  as  an  anchorage.  The  best  form  of 
construction  is  probably  a  steel  angle  in  the  corner  punched 
to  receive  rods  with  nuts  on  the  ends. 

Steel  rods  are  sometimes  laid  in  the  ground,  as  in  the 
case  of  those  used  to  tie  the  shoes  of  steel  arches  together 
in  such  structures  as  train  sheds.  To  protect  these  from 
corrosion  a  good  plan  is  to  wrap  them  in  canvas  soaked  in 
Portland  cement  grout  and  then  to  paint  the  canvas  thick- 
ly with  grout. 

Handling  and  Placing  Concrete. 

After  concrete  is  taken  from  the  mixer  or  the  mixing 
platform  it  should  be  placed  as  soon  as  possible  in  the 
forms.  As  a  rule  the  sooner  it  is  placed  the  better.  There 
is,  however,  a  possible  exception  to  this  rule.  It  is  found 
that  concrete  that  is  placed  under  water  is  less  liable  to 
have  the  cement  washed  out  of  it,  if  it  be  allowed  to  stand 
even  for  a  period  of  two  hours  or  more  before  being 
placed.  It  should,  however,  be  mixed  again  before  being 
deposited.  Concrete  placed  under  water  would  in  general 
be  in  a  thick  mass,  so  that  any  weakening  due  to  partial 
setting  before  being  placed  would  not  be  of  so  much  con- 
sequence as  it  would  be  in  such  work  as  reinforced  con- 
crete. 

It  has  been  found  also  that  retempered  concrete  will 
adhere  better  to  concrete  that  is  set  or  partially  set  than 
freshly  mixed  concrete. 

Generally  concrete  should  be  placed  in  less  than  ^  hour 
after  mixing.  It  should  not  be  disturbed  more  than  abso- 
lutely necessary  after  being  put  in  place.  If  a  receptacle 
is  used  to  hold  the  mixed  concrete  temporarily,  the  con- 
crete should  be  taken  out  of  it  in  the  order  in  which  it  is 
put  in.  If  delay  occurs  in  the  placing  of  the  concrete 

76 


that  results  in  leaving  a  batch  mixed  but  not  placed  be- 
fore the  end  of  half  an  hour,  generally  the  mixed  concrete 
should  be  rejected.  However,  if  it  is  thoroughly  re-mixed, 
adding  a  little  water,  if  necessary,  it  may  be  made  quite 
good  for  the  purpose.  It  is  found  that  retempered  con- 
crete is  almost  as  good  as  freshly  mixed  concrete,  if  the 
second  mixing  is  well  done.  For  walls  and  heavy  work, 
re-tempered  concrete  would  not  be  objectionable.  In  col- 
umns and  floors  the  uniformity  should  not  be  disturbed  by 
using  an  occasional  batch  of  concrete  that  has  received  a 
different  treatment  from  the  rest  of  the  work. 

Jarring  of  the  concrete  in  wheeling  from  the  mixer  to 
the  forms  should  be  avoided.  This  jarring  will  tend  to 
separate  the  stone  from  the  mortar.  The  runway  for  the 
wheeling  should  be  smooth.  The  concrete  should  not  be 
dropped  far  from  the  mixer,  to  the  wheelbarrows  or  carts, 
as  this  also  separates  the  ingredients. 

The  mixer  should  be  placed  high  and  the  ingredients 
raised  to  it,  so  that  the  concrete  will  not  have  to  be  lifted 
after  it  is  discharged  from  the  mixer.  The  concrete  should 
be  handled  as  little  as  possible  after  leaving  the  mixer. 

After  the  concrete  is  placed  it  should  be  left  undisturbed 
until  it  has  received  a  hard  set.  To  this  end  care  must 
be  used  in  placing  concrete  beside  other  concrete  that  is 
partially  set.  Jarring  the  projecting  steel  rods  with  the 
buckets  or  carts  in  placing  fresh  concrete  will  impair  the 
bond  of  work  that  is  partially  set.  Wheeling  carts  over 
newly  laid  floors  will  have  the  same  result.  The  work 
should  be  planned  so  that  concrete  farthest  from  the  mix- 
er will  be  deposited  first  so  as  to  avoid  this. 

Jarring  the  forms  by  the  buckets  or  carts  in  which  the 
concrete  is  handled  must  also  be  avoided.  In  putting  in 
concrete  piles  the  driving  of  the  core  for  a  pile  near  one 
that  has  lately  been  placed  may  disturb  the  latter.  Walk- 
ing over  newly  laid  concrete  should  be  avoided  as  much 
as  possible. 

The  amount  of  concrete  that  should  be  placed  at  once 
depends  upon  the  kind  of  construction  and  the  kind  of 


concrete.  Comparatively  dry  mixtures,  which,  in  general, 
should  only  be  used  in  massive,  unreinforced  work,  should 
be  placed  in  layers  of  about  6  inches  of  thickness  and  ram- 
med. In  such  work  concrete  may  be  carried  in  half  cubic 
yard  or  cubic  yard  buckets,  handled  with  a  derrick. 

In  reinforced  concrete,  where  semi-liquid  concretes  must 
be  employed,  it  is  important  that  the  concrete  be  poured  in 
such  way  and  in  such  amounts  as  not  to  cause  air  pockets 
to  form.  The  same  is  true  of  any  concrete  that  is  to  be 
impermeable.  Ramming  is  not  essential  in  such  concretes. 
In  fact,  if  the  concrete  is  of  such  consistency  that  it  can 
be  rammed,  it  is  unsuitable  for  the  purpose.  In  narrow 
forms  only  small  quantities  should  be  dumped  at  a  time. 
The  liquid  concrete  should  be  stirred  and  worked  around 
so  as  to  make  it  flow  into  the  corners  and  around  the  rein- 
forcing steel. 

If  large  quantities  of  concrete  are  placed  at  a  time  or 
in  one  place  in  reinforced  concrete  work,  it  may  cause 
springing  of  the  forms,  or  it  may  bend  or  displace  the  re- 
inforcing rods  or  any  rods  that  are  used  to  brace  the 
forms. 

Columns  more  than  about  twelve  feet  high  should  be 
poured  from  a  point  half  way  up,  so  that  the  concrete  will 
not  have  so  far  to  drop  and  so  that  puddling  of  the  con- 
crete around  the  reinforcement  can  better  be  effected.  Then 
the  doors  left  for  this  purpose  can  be  closed  and  the  re- 
mainder of  the  column  poured.  Special  care  is  needed  in 
puddling  the  concrete  in  columns  to  make  it  flow  around 
the  reinforcing  rods. 

Large  quantities  and  thick  layers  of  wet  concrete  may  be 
placed  at  once  in  mass  work,  if  it  can  be  done  without' 
leaving  air  pockets.  The  reason  for  ^comparatively  thin 
layers  in  rammed  work  is  so  that  the  ramming  will  be 
effective. 

Cinder  concrete  should  be  tamped  lightly  if  at  all,  as 
heavy  tamping  or  ramming  will  break  the  cinders.  A  wet 
mixture  is  most  suitable  for  concrete  made  with  cinders. 

It  is  often  necessary  in  exposed  work  to  spade  the  con- 

78 


crete  against  the  forms  so  as  to  work  back  the  large  stones 
and  to  bring  the  mortar  to  the  surface.  If  thick  layers 
are  deposited  at  once,  this  cannot  well  be  done,  and  the 
appearance  will  suffer. 

If  one  or  more  batches  of  concrete  are  too  wet,  as  ex- 
hibited by  free  water  on  the  concrete  after  being  placed, 
a  comparatively  dry  batch  or  more  should  be  mixed  to  take 
up  the  surplus  water. 

Rammed  concrete  should  be  placed  in  layers  approxi- 
mately horizontal.  If  this  kind  of  concrete  is  used  in 
arches  the  layers  ought  to  be  normal  to  the  line  of  thrust. 
This  is  difficult  to  do  without  setting  up  temporary  forms 
normal  to  the  arch  ring  and  tamping  beside  these.  This 
is  an  argument  for  the  use  of  wet  concrete  in  arches. 
With  wet  concrete  it  is  not  important  to  have  the  layers 
normal  to  the  line  of  thrust  except  at  quitting  time.  Where 
it  is  possible,  the  work  should  be  planned  so  that  the  en- 
tire ring  of  an  arch  can  be  poured  without  intermission. 
Another  satisfactory  plan  is  to  lay  successive  rings  end- 
ing each  against  a  temporary  vertical  partition.  This  could 
be  removed  in  a  day  or  two,  when  the  concrete  would  still 
be  green  enough  for  the  next  ring  to  adhere  pretty  well 
Another  plan  is  to  pour  half  of  the  arch  ending  it  with  a 
vertical  surface  at  the  crown. 

In  exposed  walls  the  layers  should  be  kept  higher  on  the 
face  especially  where  there  is  any  tamping.  Tamping 
brings  the  cement  to  the  surface  and  this  makes  a  relative- 
ly impervious  layer.  If  this  layer  slopes  out  toward  the 
face,  any  water  in  the  concrete  will  be  shed  outward,  car- 
rying with  it  any  dissolved  salts  to  the  face  of  the  wall. 
The  evaporation  of  this  water  leaves  the  salts  as  an  efflor- 
escence on  the  wall. 

It  is  important  that  concreting  be  stopped,  when  discon- 
tinued, at  a  joint  where  the  strength  is  not  impaired.  To  ef- 
fect this  the  finishing  surface,  as  stated,  should  be  normal  to 
the  line  of  thrust  and  it  should  not  be  where  there  is  any 
considerable  shear.  In  a  column  the  surface  should  be 
horizontal  and  below  the  line  where  beams  join  in.  It  is 

79 


preferable  to  pour  the  columns  some  hours  before  the 
beams  and  girders  so  as  to  allow  some  time  for  settlement 
and  shrinkage.  It  is  better  to  pour  an  entire  floor  at  once, 
but  if  stops  must  be  made,  they  are  best  made  at  the  mid- 
dle of  the  span  of  a  beam  or  slab  the  latter  being  on  a  line 
parallel  with  the  beams;  both  should  be  against  vertical 
surfaces.  A  beam  should  not  stop  off  near  the  support, 
as  the  shear  is  great  at  such  section.  Where  a  beam  and 
slab  are  figured  as  a  T  beam,  both  should  be  poured  at 
once.  Where  the  beam  is  figured  as  rectangular,  it  is  not 
so  important  that  both  be  placed  at  once ;  however,  it  is 
better,  as  the  full  depth  of  beam  includes  part  of  the  slab. 
A  notch  could  be  left  for  the  support  of  the  slab,  and  thus 
nearly  all  of  the  beam  would  be  placed  at  one  time. 

Some  engineers  advocate  splitting  a  beam  or  girder  in 
two  in  the  middle,  longitudinally,  by  a  temporary  vertical 
bulkhead,  when  it  is  necessary  to  stop  in  the  neighborhood 
of  a  beam  or  girder.  The  author  would  not  recommend 
chis,  but  would  rather  leave  a  step  the  depth  of  the  slab, 
an  inch  or  two  wide,  at  the  top  of  the  beam.  The  slab 
would  find  support  on  this  step,  and  if  the  beam  is  figured 
as  a  rectangular  beam  as  it  should  be  and  not  as  a  T 
beam,  it  can  borrow  from  the  other  slab  for  what  may  be 
lacking  in  bond  at  the  step.  In  a  properly  designed  beam 
carrying  slabs  there  will,  of  necessity,  be  an  excess  of  com- 
pression area.  It  is  better  to  rely  upon  this  than  to  go  to 
the  trouble  and  expense  of  fitting  a  bulkhead  along  the 
center  plane  of  a  beam,  with  all  of  the  added  difficulties 
this  entails,  such  as  narrowing  up  the  space  to  work  in, 
possible  displacing  of  the  steel,  different  degrees  of  shrink- 
age contraction  in  the  beam,  etc. 

In  enclosing  steel  work  concreting  should  not  be  stopped 
at  or  near  a  broad  horizontal  surface  of  steel,  as  the  con- 
crete will  shrink  away  from  the  steel,  and  the  thin  crack 
cannot  be  filled  up.  It  is  best  to  stop  several  inches  be- 
low or  above  such  surfaces. 

In  walls,  where  possible,  the  stop  should  be  made  at 
a  horizontal  or  vertical  bead  or  groove,  so  that  the  line 

80 


at  the  junction  of  two  days  work  will  not  show.  There 
are  several  advantages  in  placing  walls  in  short  lengftis 
at  a  time.  Vertical  joints  do  not  show  up  so  bad  as  hori- 
zontal ones,  especially  when  these  are  made  by  use  of  a 
bulkhead  and  are  true  to  line.  The  contraction  of  the  con- 
crete due  to  setting  will  be  equalized  as  the  wall  progresses. 
These  vertical  joints  will  often  be  sufficient  to  take  up  ex- 
pansion and  contraction  due  to  change  in  temperature. 
The  mixing  plant  can  be  moved  from  section  to  section, 
thus  lessening  the  distance  through  which  mixed  concrete 
must  be  carried. 

Before  starting  to  place  concrete  it  is  important  to  see 
that  the  forms  are  clean.  The  bottoms  of  boxes  for  beams 
and  girders  and  the  bottoms  of  columns  should  be  cleared 
of  all  dirt,  sawdust,  shavings,  blocks  of  wood,  etc.  Blocks 
of  wood  may  have  lodged  among  the  reinforcing  rods  of 
walls  or  columns.  These  must  be  removed. 

It  is  important  to  have  the  forms  finished  far  enough 
in  advance  of  the  placing  of  the  concrete  to  insure  continu- 
ity of  the  concreting. 

When  leaving  off  the  placing  of  concrete  for  the  day 
care  should  be  taken  to  see  that  the  finishing  surface  is 
left  so  that  the  conditions  of  continuous  work  are  approxi- 
mated as  near  as  possible.  The  bonding  of  the  next  days' 
work  should  be  made  as  good  as  the  conditions  will  permit. 
It  is  better,  in  general,  to  leave  the  surface  rough  than 
smooth.  In  heavy  work  a  bond  may  be  made  in  several 
ways.  One  way  is  to  make  steps  in  the  top  by  setting  up 
vertical  boards  and  tamping  against  them.  Another  way 
is  to  bed  large  stones  half  in  the  last  layer  of  concrete 
allowing  the  other  half  to  project  into  the  new  concrete. 
Still  another  method  is  to  lay  wooden  blocks  in  the  con- 
crete to  form  recesses  and  remove  them  before  the  next 
day's  work  begins. 

In  reinforced  concrete  work  and  in  impermeable  con- 
crete dependence  must  be  placed  more  upon  treatment  of 
the  surface  before  starting  to  lay  concrete  than  on  rough- 
ening it  at  quitting  time.  It  is  important  in  any  work  that 

81 


the  surface  be  clean.  Also  the  forms  should  be  cleaned  of 
any  concrete  that  has  been  spattered  on  the  day  before. 
Picking  over  the  surface  with  picks,  if  it  has  stood  long, 
is  recommended  to  remove  the  top  skin.  Washing  the 
surface  with  a  hose  and  brooming  or  brushing  it  would 
be  sufficient,  where  it  has  not  stood  very  long.  This  wash- 
ing of  the  surface  of  the  last  day's  placing  of  concrete  is 
very  useful  to  get  rid  of  the  laitance  or  slime  that  comes 
to  the  surface.  It  serves  to  lessen  danger  of  efflorescence 
and  to  make  a  better  bond.  The  bond  will  be  strengthened 
by  brushing  over  a  thin  coat  of  grout  of  neat  cement  or  by 
sifting  neat  cement  on  the  previously  moistened  surface. 
Bond  to  old  and  hardened  concrete  is  effected  by  this  same 
means. 

Much  cement  pavement  work  is  being  done  in  Pittsburg 
by  picking  over  the  worn-out  flag  stone  pavement  to  two 
inches  or  so  below  the  desired  new  level,  moistening  the 
surface,  dusting  on  neat  cement  and  spreading  the  same 
with  a  broom,  and  then  laying  cement  mortar  to  the  de- 
sired level. 

When  concrete  is  placed  in  contact  with  bricks  or  porous 
tile,  these  should  be  thoroughly  saturated  so  as  to  im- 
prove the  bond  and  to  prevent  the  absorption,  by  the  por- 
ous substances,  of  the  water  in  the  concrete. 

A  very  good  grade  of  concrete  blocks  or  artificial  stone 
can  be  made  by  casting  the  blocks  in  sand  as  iron  cast- 
fngs  are  made.  The  mixture  must  be  very  wet,  a  consist- 
ency that  would  be  called  soupy.  The  surplus  water  is 
absorbed  by  the  sand,  and  this  serves  to  keep  the  block 
moist  during  setting.  By  using  a  well  selected  aggregate, 
such  as  crushed  marble,  crushed  granite,  white  sand,  etc., 
excellent  artificial  stone  can  be  made.  The  product  is 
dense  and  uniform,  because  the  concrete  is  not  dry  and 
tamped,  and  because  varying  atmospheric  conditions  have 
no  effect  upon  it  while  it  is  setting.  These  artificial  stone 
blocks  are  usually  cast  smooth  and  then  tooled  on  the  sur- 
face by  tools  operated  by  power.  A  pleasing  surface  is 
made  by  the  use  of  carborundum  wheels.  If  reinforced 

82 


with  steel,  the  blocks  may  be  made  quite  thin,  even  down 
to  iVz  or  2  ins.  Blocks  not  reinforced,  used  for  veneering, 
are  usually  3  or  4  in.  thick.  The  blocks  should  remain 
in  the  sand  4  to  6  days,  and  should  then  season  for  about 
two  weeks  before  being  used. 

Fine  details  in  ornamental  work  will  be  more  satisfactory 
if  cast  in  sand  with  very  wet  mixtures  than  in  many  other 
kinds  of  molds  or  with  dry  mixtures. 

Concrete  blocks  can  be  made  of  a  medium  mixture,  mold- 
ed under  heavy  pressure.  Because  of  the  pressure  they 
can  be  removed  from  the  mold  immediately.  The  blocks 
are  denser  and  better  in  every  way  than  the  hand  tamped 
blocks  made  from  a  dry  mixture. 

Large  concrete  blocks  are  often  cast  near  the  point  where 
they  are  to  be  placed  in  a  structure  in  suitable  forms  of 
wood  or  sheet  steel  or  other  material.  When  hardened, 
they  are  lifted  into  place.  Very  heavy  blocks  can  have 
rings  cast  in  them  to  facilitate  handling.  These  blocks 
may  be  used  for  breakwater  construction,  sea  walls,  arches, 
etc.  In  sewer  construction  curved  blocks  can  be  cast  and 
the  necessity  of  expensive  arch  forms  and  lagging  avoid- 
ed. The  arch  blocks  can  be  held  in  place  by  the  side 
blocks,  and  little  or  no  centering  is  required.  In  like  man- 
ner reinforced  concrete  slabs  can  be  cast  separately  for 
the  top  of  a  sewer,  and  as  these  exert  no  thrust  the  side 
walls  can  be  thinner. 

The  casting  of  reinforced  concrete  slabs  may  often  be 
found  to  effect  a  saving  in  the  construction  of  sidewalks 
and  floors.  These  can  be  cast  one  over  the  other  with 
some  kind  of  a  separating  medium  and  lifted  into  place 
when  hardened. 

Beams  and  columns  have  likewise  been  cast  on  the 
ground  and  lifted  to  place.  In  general  this  is  a  doubtful 
expedient.  The  importance  of  the  beams  and  columns  of  a 
structure  being  tied  together  as  a  unit  is  very  great,  un- 
less the  walls  of  the  structure  supply  all  of  the  lateral 
rigidity. 

83 


Concrete  piles  are  made  both  by  casting  them  in  place 
or  casting  them  on  the  ground  and  then  driving.  In  the 
first  method  the  hole  for  the  pile  may  be  made  by  driving 
a  wooden  pile  and  withdrawing  it;  or  it  may  be  made  by 
driving  a  collapsible  core  with  a  sheet  metal  shell  and  fill- 
ing this  shell  with  concrete;  or  it  may  be  made  by  driving 
a  steel  tube  with  a  removable  driving  point  and  filling  the 
hole  with  concrete  as  this  tube  is  drawn  up.  In  any  of 
these  methods  the  concrete  should,  in  general,  be  well  ram- 
med so  as  to  insure  filling  of  the  hole  and  the  ability  of 
the  pile  to  take  a  load  without  settlement.  Piles  that  are 
cast  before  being  driven  should  be  cast  upright,  if  made 
of  dry  concrete,  so  that  the  joint  between  the  layers  will 
be  normal  to  the  direction  of  the  driving.  In  wet  concrete 
it  is  not  important  whether  the  piles  are  cast  horizontal 
or  vertical.  However,  unless  they  are  well  reinforced  it 
is  difficult  to  raise  long  piles  to  the  vertical  position.  As 
far  as  practicable,  the  length  of  these  piles  should  be 
known  before  they  are  driven,  as  it  is  not  practicable  to 
splice  them,  and  it  is  difficult  and  expensive  to  cut  them. 
In  driving  concrete  piles  a  hammer  weighing  nearly  as 
much  as  the  pile  and  having  a  short  fall  is  needed.  The 
blow  of  a  light  hammer  will  be  absorbed  locally  and  shat- 
ter the  pile.  Concrete  piles  should  stand  two  weeks  or 
more  of  good  weather  before  being  driven.  Concrete 
piles  should  be  larger  in  diameter  and  generally  fewer 
in  number  than  wooden  piles  for  the  same  structure. 

In  placing  concrete  under  water  it  is  important  that 
it  be  treated  in  such  way  that  the  cement  of  the  concrete 
will  not  be  washed  out.  Dropping  concrete  through  a 
depth  of  water  will  not  only  wash  out  some  of  the  cement 
but  will  tend  to  separate  the  ingredients.  Concrete  should 
not  be  rammed  under  water,  as  the  stirring  of  the  water 
will  carry  away  cement.  It  should  not  be  deposited  in 
running  water. 

If  concrete  is  to  be  placed  in  water,  it  should  be  placed 
in  as  large  batches  as  possible.  It  should  be  wet  concrete, 
so  as  to  require  no  ramming.  It  should  be  mixed  long. 

84 


Concrete  that  is  mixed  and  allowed  to  stand  several  hours 
and  then  mixed  again  is  said  to  be  preferable  to  freshly 
mixed  concrete  for  placing  under  water,  as  the  cement  is 
partially  set  and  is  less  liable  to  be  washed  out.  It  is 
well  to  use  about  ten  per  cent,  extra  cement  for  the  con- 
crete that  is  to  be  placed  under  water  to  allow  for  loss. 

The  concrete  may  be  lowered  in  steel  buckets  with  bot- 
tom doors  that  are  opened  when  the  bucket  reaches  the 
bottom.  Canvas  sacks  may  also  be  employed.  These  sacks 
are  lowered  with  the  mouth  down.  This  is  tied  shut  in 
such  way  that  it  may  be  tripped  open  with  a  line.  A  bet- 
ter way  to  place  the  concrete  is  to  let  it  down  through  a 
tube  or  tremie.  This  should  be  kept  full  of  concrete,  the 
lower  end  resting  on  the  bottom  and  being  moved  about 
so  as  to  distribute  the  concrete. 

Reinforced  concrete  should,  in  general,  not  be  placed 
under  water.  Any  concrete  reinforced  with  steel  that  will 
be  submerged  during  setting  and  subsequently  should  be 
designed  so  that  no  dependence  will  be  placed  upon  the  ad- 
hesion or  grip  exerted  between  the  concrete  and  steel.  Con- 
crete setting  under  water  does  not  shrink  and  grip  the  steel 
as  that  which  sets  in  air.  The  rods  should  have  nuts  on 
the  ends  and  washer  plates  or  some  other  effective  end 
anchorage.  A  riveted  structure  under  water  embedded  in 
concrete  for  its  protective  value,  is  legitimate  construction, 
if  the  concrete  is  of  sufficient  mass  not  to  be  cracked  by 
differential  expansion. 

When  grout  is  to  be  used  under  water,  as  in  filling  inter- 
stices in  stone  work,  cracks  in  concrete,  etc.,  neat  cement 
should  be  employed,  as  sand  will  separate  from  a  mixture 
of  sand  and  cement  in  passing  through  water. 

Concrete  should  not  be  deposited  in  polluted  water,  as 
that  containing  sewage  or  discharge  from  pulp  mills  or 
refuse  from  other  washing  processes.  Such  water  com- 
ing in  contact  with  fresh  concrete  will  destroy  it  by  at- 
tacking the  setting  cement. 

In  constructing  inverts,  such  as  the  curved  bottoms  of 
filter  beds,  sewers,  etc.,  it  is  often  best  to  omit  the  lag- 
85 


ging  as  far  up  the  side  of  the  curve  as  the  concrete  will 
permit  without  sloughing.  The  arch  forms,  however 
should  be  in  place  to  serve  as  guides  in  finishing  the  sur- 
face. By  omitting  the  lagging  the  concrete  can  be  com- 
pacted better,  and  a  better  surface  finish  can  be  obtained. 

Much  time  and  labor  could  be  saved  in  the  making  of 
concrete  if  the  broken  stone  or  gravel  could  be  placed  with- 
out having  to  pass  it  through  the  mixer  or  having  to  pick 
it  all  up  in  shovels  and  turn  it  a  half  a  dozen  times  or 
more.  Such  a  process  would  not  be  productive  of  the 
best  grade  of  concrete  because  of  the  many  chances  of 
air  pockets  being  left  and  of  lack  of  bond  with  the  stone 
due  to  failure  of  the  grout  to  flow  beneath  the  stones. 
There  are  some  situations,  however,  in  which  the  kind  of 
concrete  resulting  from  this  process  would  meet  all  of  the 
requirements.  This  method  of  laying  concrete  for  street 
pavements  is  described  in  Concrete  Engineering,  Apr.  15, 
1907,  in  a  paper  written  by  Mr.  Walter  E.  Hassam.  The 
method  there  described  is  as  follows.  First  the  subgrade 
is  rolled  to  an  elevation,  for  ordinary  street  paving  in 
concrete,  about  6  inches  below  the  finished  surface.  Then 
broken  stone  of  the  egg  size  is  spread  to  a  sufficient  depth 
so  that  after  rolling  it  will  be  2  inches  below  the  finished 
grade  of  the  street.  The  following  is  quoted  from  Mr. 
Hassam's  paper. 

"This  foundation  stone  is  rolled  or  compressed  until 
thoroughly  compact,  and  the  voids  reduced  to  a  minimum. 
It  is  then  treated  with  a  grout,  composed  of  one  part  of 
cement  to  4  of  sand.  This  grouting  and  rolling  is  contin- 
ued, until  all  the  voids  are  completely  filled.  This  pro- 
cess gives  an  exceedingly  dense  concrete,  which  is  very 
strong. 

"For  the  wearing  surface,  there  is  spread  upon  the 
foundation,  before  it  has  set,  sufficient  stone,  of  the  stove 
size,  to  bring  the  street  to  the  required  grade  after  roll- 
ing. This  stone  is  uniformly  rolled  or  compressed,  until 
embedded  in  and  united  with  the  foundation.  Then  it 


is  given  a  thin  grouting  of  Portland  cement  and  sand, 
mixed  in  the  proportion  of  I  cement  to  2  sand. 

"The  voids  are  thoroughly  filled  with  grouting,  and  then 
the  surface  is  rolled  until  the  grout  flushes  to  the  top  of 
the  stone.  As  a  finish,  there  is  then  applied  a  thin  layer 
of  creamy  cement  and  pea  stone  mixed  in  the  propor- 
tion of  I  cement,  I  sand  and  I  of  pea  stone. 

"This  surface  is  poured  on,  brushed  and  rolled  to  an 
even  surface.  The  street  is  then  allowed  to  set  for  at 
least  6  days,  when  it  is  ready  for  traffic.  The  layers  fol- 
low each  other  so  closely  that  the  foundation  does  not  set 
until  the  whole  is  complete.  When  complete,  the  entire 
road  is  a  solid,  homogeneous  mass  of  rock  and  cement, 
that  will  resist  anything  that  can  possibly  come  in  contact 
with  it. 

"The  finished  surface  of  the  pavement  presents  to  the 
casual  observer  a  smooth  and  fine  appearance,  but,  on 
close  examination,  it  is  found  to  be  somewhat  rough,  so 
there  will  be  no  slipping  of  horses  or  skidding  of  auto- 
mobiles." 

The  above  is  the  method  of  laying  concrete  used  with 
success  in  Worcester,  Mass.  It  may  be  used  for  the  con- 
crete foundation  of  a  brick  or  block  pavement  of  any  kind 
or  alone  for  solid  concrete  pavement.  In  a  note  regarding 
these  same  pavements,  in  the  Engineering  Record,  Vol. 
53,  p.  625,  it  is  stated  that  for  a  cement  wearing  surface  a 
thick  grout  of  sand  and  cement  is  poured  over  the  founda- 
tion (of  rolled  stone)  and  immediately  filled  with  fine 
crushed  stone  and  rolled. 

It  is  certain  that  concrete  made  as  above  described,  with 
thorottgly  mixed  grout,  would  be  equal  to  if  not  superior 
to  the  half  mixed  commercial  concrete  that  often  goes 
into  our  city  streets.  The  rolling  and  consequent  compact- 
ing of  the  broken  stone  before  applying  the  grout  produces 
a  foundation  that  is  capable  of  supporting  considerable 
load  without  the  aid  of  the  cementing  grout. 

Other  cases  where  concrete  may  be  made  in  place,  with- 
out handling  the  broken  stone  in  the  mixer  are  in  rough 

87 


r 


retaining  walls  or  breakwaters.  In  these  the  grout  may  be 
introduced  by  inserting  steel  pipes  at  intervals  and  forc- 
ing the  liquid  mortar  into  the  voids,  either  by  gravity  or 
by  air  pressure. 

The  Setting  and  Hardening  of 
Concrete. 

It  is  important  that  concrete  be  free  from  jar  or  disturb- 
ance during  setting.  It  should  not  be  subject  to  intense 
cold  or  high  heat.  Water  in  small  interstices,  as  in  the 
body  of  concrete,  will  not  freeze  at  32  degrees;  but  it  will 
freeze  at  a  somewhat  lower  temperature.  If  the  mater- 
ials can  be  kept  above  the  freezing  temperature  until  the 
concrete  is  placed,  danger  of  freezing  is  lessened  by  the 
heat  evolved  in  the  cement  during  the  process  of  initial 
set;  so  that  temperature  higher  than  about  25  degrees  can 
be  worked  in  without  much  danger.  This  is  especially  true 
of  concrete  in  thick  masses.  In  thin  walls  or  slabs  the  heat 
generated  will  be  quickly  lost  and  protection  is  needed. 

Protection  of  setting  concrete  may  be  afforded  by  the 
use  of  tar  paper  or  canvas  or  boards  laid  over  it.  A  foot 
or  so  of  hay  is  good  for  this  purpose.  Two  layers  of  can- 
vas or  tar  paper,  separated  by  boards,  will  give  very  ma- 
terial protection.  If  only  a  single  layer  is  used,  it  should 
not  be  allowed  to  touch  the  concrete,  but  should  be  kept 
out  by  boards.  If  manure  is  used,  it  should  not  be  al- 
lowed to  come  in  contact  with  the  concrete,  and  it  should 
not  be  allowed  to  become  wet.  Water  that  has  absorbed 
elements  from  the  manure  is  apt  to  be  injurious  to  the 
setting  concrete  and  to  cause  it  to  rot  and  be  useless.  Ce- 
ment bags  or  tar  paper  used  for  protection  should  be  well 
lapped. 

Placing  of  concrete  in  temperatures  below  25  degrees 
should  be  avoided  where  possible.  If  it  must  be  done,  the 
best  thing  to  do  is  to  enclose  the  work  with  canvas  and 
heat  the  enclosed  space  with  salamanders,  or  better  with 
steam.  The  concrete  should  be  protected  from  the  direct 

88 


heat  of  any  kind  of  stoves,  so  that  it  will  not  be  dried  out 
too  soon  and  prevented  from  setting. 

Though  concrete  that  has  been  allowed  to  freeze  and 
afterwards  to  thaw  has,  after  having  had  time  enough  to 
set,  taken  on  apparently  the  strength  of  properly  treated 
concrete,  it  is  not  safe  to  rely  on  concrete  thus  treated 
in  any  structure  where  strength  is  an  essential  feature. 
Freezing  should  be  avoided  and  prevented  by  means  that 
will  not  heat  up  the  concrete  and  cause  drying  out.  The 
use  of  salt  in  the  water  is  not  recommended.  Anything 
short  of  a  strong  brine  would  freeze  at  a  temperature  not 
much  below  32  degrees,  and  the  possibilities  of  efflorescence 
and  of  corrosion  of  embedded  steel  make  the  use  of  salt 
an  undesirable  risk. 

While  thoroughly  seasoned  limestone  concrete  may  stand 
400  to  500  degrees  F.  without  any  detriment  or  change  of 
structure,  and  other  concretes  may  stand  more,  it  is  not 
safe  for  it  to  be  subject,  while  setting  and  hardening,  to  a 
heat  that  will  evaporate  the  contained  water.  The  pres- 
ence of  water  is  necessary  to  the  hardening  of  the  cement, 
and,  if  it  be  robbed  of  this  water,  it  will  suffer  in  strength. 

Concrete  that  is  setting  will  suffer  from  other  than 
thermal  conditions  which  would  not  effect  seasoned  con- 
crete. Water  containing  decaying  organic  matter,  sewage, 
the  discharge  from  pulp  mills,  etc.  will  rot  setting  concrete, 
though  these  substances  will  not,  in  general,  have  a  dele- 
terious effect  on  hardened  concrete.  Some  oils  will  weak- 
en setting  concrete  which  could  be  safely  stored  in  con- 
crete tanks. 

Water  is  necessary  to  the  hardening  of  cement.  The 
water  of  mixing,  if  it  be  a  liberal  quantity,  is  sufficient  for 
this  purpose  in  some  cases,  as  when  the  concrete  is  in  a 
damp  place;  but  it  is  generally  best,  and  sometimes  neces- 
sary to  the  safety  of  the  structure  or  the  integrity  of  the 
concrete,  to  add  water  during  setting.  Concrete  should  be 
covered  and  protected  from  the  rays  of  the  sun  and  from 
wind  to  prevent  evaporation  of  the  water.  Concrete 
blocks  (the  kind  that  are  made  of  a  concrete  having  the 


consistency  of  "moist  earth"  and  tamped  in  molds,  and 
from  which  the  molds  are  immediately  removed)  are 
greatly  improved  and  made  to  approach  the  condition  of 
good  concrete,  if  they  are  immediately  soaked,  upon  re- 
moval from  the  forms,  by  allowing  a  smooth  stream  of 
water  under  no  pressure  to  run  upon  them  until  they  will 
take  in  no  more.  Generally  these  blocks  are  kept  sprink- 
led with  a  little  water  for  several  days  to  "cure"  them. 
It  would  be  better  to  use  preventive  measures  and  fore- 
stall the  ailment  by  mixing  them  with  plenty  of  water  and 
allowing  the  molds  to  remain  until  the  concrete  will  stand 
up.  Not  much  can  be  expected  of  a  block  so  porous  as 
to  turn  dark  gray  after  a  rain,  even  if  cellular  construc- 
tion does  keep  the  inside  of  the  wall  comparatively  dry. 
Disintegration  is  almost  sure  to  get  in  its  work.  No  nat- 
ural stones  that  are  not  compact  would  be  acceptable  for 
building  work. 

Rich  mixtures  of  concrete  need  especially  to  be  kept 
moist  during  setting,  as  these  are  more  apt  to  shrink  and 
crack  on  the  surface  or  in  the  body  of  the  concrete.  A 
rich  mortar  finish  or  a  troweled  surface  should  be  kept 
wet  for  nearly  a  week  and  protected  from  winds  and  sun 
to  insure  its  solidity. 

Any  thin  coating  of  mortar  or  grout  should  not  only  be 
put  on  a  thoroughly  saturated  surface,  but  should  be  lib- 
erally wetted  for  a  day  or  two.  Such  coatings  are  apt  to 
have  their  water  absorbed  by  the  wall  or  evaporated  and 
to  lose  their  cohesion. 

When  a  concrete  wall  or  pier  is  placed  in  a  cofferdam,  it 
is  well  to  let  in  the  water  around  it  a  day  after  the  con- 
crete is  placed.  Concrete  requires  longer  to  set  under 
water  than  in  the  air,  but  it  acquires  greater  strength. 
Specimens  that  have  hardened  in  water  will  show  much 
greater  strength  than  those  that  have  hardened  in  the  air. 
Immersion  in  water  should  be  delayed  until  initial  set 
takes  place.  Moistening  concrete  will  delay  the  setting  to 
some  extent.  This  should  be  taken  into  account  in  gag- 

00 


ing  the  time  to  remove  the  molds.  Humidity  in  the  at- 
mosphere acts  in  some  degree  like  immersion  in  water. 

The  time  that  should  elapse  between  the  placing  of  con- 
crete and  the  removal  of  the  forms  depends  upon  a  num- 
ber of  things,  among  which  are  the  consistency  of  the  con- 
crete, the  richness  of  the  mixture,  the  load  sustained,  and 
the  temperature  and  atmospheric  humidity.  Wet  concretes 
require  longer  to  harden  than  dry  concretes.  Lean  con- 
cretes require  longer  than  rich  ones.  Concrete  hardens 
more  slowly  under  water  or  in  a  saturated  atmosphere 
than  in  dry  air.  Low  temperatures  delay  the  setting  of 
concrete.  If  the  temperature  be  below  freezing,  the  sett- 
ing may  be  suspended.  Failures  have  resulted  on  account 
of  forms  being  removed  from  concrete  that  was  frozen 
and  appeared  to  be  hardened  due  to  setting. 

Another  error  apt  to  be  made  is  to  mistake  drying  for 
setting.  Drying  is  not  a  necessary  accompaniment  to  the 
hardening  of  concrete.  In  fact  if  the  concrete  is  too  warm 
and  the  air  too  dry  the  early  drying  of  the  concrete  that 
will  result  will  be  detrimental  to  its  strength.  Concrete 
should  not  be  allowed  to  dry  out  until  it  has  stood  for 
several  days.  Sidewalks  should  be  sprinkled  for  four 
or  five  days.  They  should  be  covered  and  protected  from 
currents  of  air.  Plastered  work  and  reinforced  concrete 
need  special  care  in  the  matter  of  maintaining  moisture 
on  the  surface;  otherwise  shrinkage  cracks  will  develop. 

Concrete  blocks  need  frequent  and  copious  sprinkling, 
which  should  be  continued  for  a  week  or  more. 

Concrete  receives  its  set  when  it  reaches  the  state  where 
a  change  of  shape  cannot  be  produced  without  rupture. 
This  requires  from  a  few  minutes,  in  rich  mortars  of  quick 
setting  cement,  to  several  hours,  in  lean  mixtures.  A  com- 
mon way  of  determining  when  concrete  has  set  is  by  pres- 
sure of  the  thumb  nail.  After  the  set  has  taken  place  the 
concrete  continues  to  harden  and  gain  strength  for  months 
and  sometimes  for  years.  In  ordinary  weather  nearly  the 
full  strength  is  attained  in  six  or  eight  weeks.  Loading 
tests  may  be  made  at  this  stage.  Strength  necessary  to 

91 


support  its  own  weight  is  reached  at  varying  periods  de- 
pending upon  several  conditions. 

In  counting  the  time  that  concrete  should  stand  before 
removing  the  forms  days  when  the  temperature  is  at  or 
below  freezing  should  be  counted  out,  or  at  least  allow- 
ance should  be  made  for  almost  total  suspension  of  the 
hardening  process. 

It  is  safe  to  remove  the  forms  from  mass  work,  receiv- 
ing at  the  time  no  load  except  its  own  weight,  in  from  one 
to  three  days ;  in  warm  weather  with  dry  concrete,  one  day, 
in  cold  or  wet  weather  or  with  wet  concrete,  more  time. 
When  the  concrete  will  bear  the  pressure  of  the  thumb 
nail  without  indentation,  it  is  ready  to  support  itself  in 
this  class  of  work.  Thin  walls  should  stand  two  to  five 
days.  Slabs  of  reinforced  concrete  should  stand  about  one 
to  two  weeks  of  good  weather  before  being  called  upon  to 
support  their  own  weight.  Slabs  of  long  span  may  require 
more  time  than  two  weeks.  At  the  same  time  that  the  slab 
centering  is  removed,  or  even  before  it  is  taken  down,  the 
forms  on  the  sides  of  beams  and  girders  can  be  removed, 
leaving  the  supports  of  the  bottoms  in  place  for  a  longer 
time.  This  will  afford  an  opportunity  to  inspect  the  sur- 
face of  the  beams  and  girders  and  to  plaster  up  any  cavi- 
ties before  the  concrete  is  too  hard.  Where  practicable 
it  is  well  to  leave  the  shores  under  beams  and  girders  for 
three  or  four  weeks.  Large  and  heavy  beams  should  be  al- 
lowed to  stand  longer  than  short  ones,  because  the  dead 
weight  is  a  greater  fraction  of  the  load  they  are  designed 
to  carry. 

Column  forms  can  be  removed  in  a  week  or  so,  if  the 
entire  weight  of  the  beams  is  supported  by  shores  close 
to  the  columns,  otherwise  three  weeks  or  more  should  be 
allowed. 

Arches  of  small  span  can  have  the  centering  removed  in 
one  to  two  weeks.  Large  arches  should  harden  a  month  or 
more.  Where  practicable  it  would  be  well  to  leave  the 
concreting  of  the  spandrel  wall  of  an  arch  span  until  the 
arch  ring  has  hardened  and  the  forms  are  removed.  The 


settling  of  the  arch  often  cracks  the  spandrel  wall  and 
gives  an  unsightly  appearance  to  the  bridge. 

Ornamental  work  should  have  the  forms  removed  as 
soon  as  possible,  so  that  defects  can  be  plastered  up  and  so 
that  swelling  of  the  wood  will  have  less  tmie  to  act. 

Falsework  should  be  removed  carefully,  without  jar  to 
the  concrete  either  by  hammering  on  the  boards  or  drop- 
ping heavy  pieces  on  the  floor  below.  The  supports  should 
not  be  removed  when  any  unusual  load  is  on  the  floor. 
Materials  should  not  be  stored  on  floors  that  are  not  thor- 
oughly hardened  and  self  supporting. 

Concrete  in  reinforced  work  should  ring  when  struck 
with  the  hammer,  before  the  supports  are  removed. 

Finishing  Concrete  Surfaces. 

One  of  the  chief  difficulties  in  connection  with  the  use 
of  concrete  is  to  get  a  surface  finish  that  is  pleasing  iu 
appearance  and  at  the  same  time  economical.  The  various 
methods  in  use  will  be  taken  up  with  a  view  of  showing 
their  good  and  bad  features  and  their  limitations. 

Surfaces  that  are  wrought  in  other  materials  than  con- 
crete will  first  be  considered. 

A  common  and  acceptable  surface  finish  is  a  veneer  of 
brick.  Brick  work  in  4  in.  thickness  may  be  laid  against 
a  concrete  wall.  For  example,  if  a  13  in.  wall  would  be 
required,  an  8  in.  wall  of  concrete  may  be  put  up  in  the 
regular  way,  using  wooden  forms,  then  the  brick  may  be 
laid  outside  of  this.  Metal  bond  is  often  used,  small  pieces 
of  wire  or  other  metal  being  bedded  in  the  concrete  and 
projecting  out  to  be  built  into  the  brick  work.  An  other 
than  metal  bond  is  preferable.  The  metal  is  not  thorough- 
ly protected  in  a  brick  wall  because  of  the  porosity  of  the 
wall.  Occasional  belt  courses  of  cut  stone  projecting  out 
for  the  support  of  the  brick  work  would  serve  to  lessen 
the  height  of  the  unsupported  brick  veneering  and  thus 
lessen  dependence  on  metal  bond.  A  good  method  of  bond- 
ing -would  be  to  leave  vertical  recesses,  at  intervals,  about 

93 


the  width  of  a  brick.  Into  these  headers  could  be  laid  and 
thus  a  very  satisfactory  bond  secured. 

Another  way  to  have  a  brick  surface  is  to  lay  up  the 
brick  wall  and  use  it  as  the  outside  of  the  form  pouring 
the  concrete  behind  it. 

Cut  stone  and  artificial  stone  veneers  may  also  be  used 
in  the  same  way  as  brick.  This  is  satisfactory  for  a  wall 
not  taking  much  vertical  load.  It  may  lead  to  structural 
weakness,  if  used  for  a  pillar  taking  a  concentrated  load. 
More  than  one  case  could  be  cited  in  large  buildings, 
where  reliance  upon  a  combination  of  a  stone  shell  and  a 
core  of  other  material  in  a  pillar,  to  take  a  load,  necessi- 
tated the  removal  of  the  pillars  and  the  insertion  of  steel 
columns  after  the  walls  were  completed.  Cracks  in  the 
stone  veneer  showed  that  it  was  taking  the  load,  and  that 
it  was  not  capable  of  withstanding  it  In  one  building 
the  core  was  of  rubble  masonry  and  the  shell  was  of  cut 
stone;  in  another  the  core  was  of  concrete  and  the  shell 
was  of  artificial  stone.  Both  rubble  masonry  and  con- 
crete will  shrink  on  account  of  the  large  proportion  of 
mortar.  The  cut  stone  and  the  artificial  stone,  with  their 
deep  courses  and  thin  mortar  joints,  do  not  shrink  any 
perceptible  amounts.  The  result  is  that  about  all  of  the 
load  must  be  carried  by  the  veneer.  The  same  fault  has 
been  observed,  where  tile  facing  was  backed  with  brick. 
In  this  case  the  cracking  of  the  tile  was  attributed  to 
failure  of  the  mortar  to  set  because  of  the  cold  weather. 
Settling  of  the  brick  work  behind  the  weak  tile  would, 
however,  be  apt  to  produce  the  same  result  in  work  set  up 
in  warm  weather.  In  construction  of  this  sort  no  depend- 
ence whatever  should  be  placed  upon  the  veneer  in  sup- 
porting the  load,  and  it  should  be  built  in  such  way  as  to 
allow  the  core  to  shrink  in  setting.  This  might  be  effect- 
ed by  using  wooden  blocks  a  trifle  higher  than  the  stones 
for  one  or  more  courses  and  removing  these  later  and  sub- 
stituting the  stone  or  tile.  It  might  also  be  done  by  leav- 
ing out  the  top  course  of  stone  or  tile  facing.  Or  a  number 
of  the  joints  in  the  facing  might  be  raked  out,  soon  after 


the  concrete  backing  is  placed,  and,  after  the  concrete  has 
set  and  shrunk,  these  joints  could  be  pointed.  The  use 
of  dry  tamped  concrete  would  lessen  the  shrinking.  In  a 
long  wall  brought  up  slowly  the  shrinking  will  not  be  so 
harmful.  In  a  small  pillar  a  cast  iron  or  steel  column 
should  be  used  in  the  middle. 

In  the  present  state  of  the  art  artificial  stone  or  cut 
stone  facing  is  probably  the  best  surface  treatment  for 
concrete  in  such  construction  as  residences  and  office  build- 
ings. This  is  partially  due  to  the  fact  that  concrete  work- 
ers have  not  developed  the  skill  that  workers  in  the  other 
materials  possess.  Brick  work  with  the  outer  %  in.  or  so 
of  mortar  "raked  out"  (or  blocked  out  with  wooden  cleats, 
as  is  done  in  practice)  makes  an  appropriate  and  pleas- 
ing surface  finish  for  rugged  styles  of  architecture. 

Blocks  in  glazed  tile  are  made  use  of  for  external  fin- 
ish of  buildings.  With  these  it  is  even  more  important 
that  but  a  short  height  be  laid  at  once,  if  concrete  is  poured 
behind  them,  or  some  other  precaution  be  employed  to  pre- 
vent their  receiving  any  of  the  load  of  the  waif.  These 
tile  are  brittle  and  unreliable  in  supporting  loads. 

Thin  tile  can  be  used  as  an  external  finish  by  pasting 
them  on  paper,  as  they  come  for  pavements,  and  then  past- 
ing the  paper,  with  bill  posters'  paste,  on  the  inside  of  the 
forms  before  concrete  is  placed.  Before  the  forms  are 
removed  they  must  be  thoroughly  flushed  with  water. 

Boulder  facing  may  be  made  on  rustic  walls  or  arch 
spans  by  placing  the  boulders  against  the  forms  and  then 
the  concrete  behind  them. 

Of  the  surface  finishes  that  are  made  in  the  concrete 
itself  there  may  be  mentioned  those  that  are  made  in  the 
concrete  by  aid  of  the  forms,  while  it  is  being  placed,  and 
those  that  require  subsequent  treatment. 

If  the  concrete  is  simply  placed  against  the  rough  sur- 
face of  sawed  boards,  it  will  have  the  impression  of  the 
saw  marks  and  grain  and  knots  as  well  as  the  cracks  or 
joints.  This  is  far  from  pleasing  for  any  surface  above 
the  ground.  When  the  forms  against  the  exposed  face  are 

95 


made  of  planed  boards,  tongued  and  grooved,  and  neatly 
jointed,  the  surface  is  greatly  improved.  A  broad  surface 
can  be  relieved  of  its  monotony  by  paneling.  The  larger 
and  rougher  the  surface  the  bolder  the  panels  should  be. 
Long  retaining  walls  should  preferably  have  panels  to  re- 
lieve the  dead  flat  surface. 

If  the  concrete  is  thrown  indiscriminately  against  the 
forms,  the  surface  will  not  present  a  smooth  appearance, 
especially  if  dry  concrete  is  used.  By  manipulating  the 
concrete  with  spades  or  shovels  it  can  be  given  a  richer 
and  smoother  surface.  As  a  layer  of  concrete  is  placed 
a  shovel  is  run  down  against  the  form  and  the  larger  stones 
shoved  back.  This  allows  the  mortar  of  the  concrete  to 
flow  against  the  form,  and  a  surface  of  mortar  results. 
Sometimes  a  perforated  shovel  or  spade  is  used  for  this 
purpose,  and  the  mortar  passes  through  the  perforations. 
With  rammed  or  dry  concrete  the  spade  may  be  used  to 
shove  back  the  concrete  and  a  wetter  mortar  poured  in. 
Of  course  the  smoother  the  forms  for  this  class  of  work 
the  better  will  be  the  appearance  of  the  work. 

In  narrow  forms  it  is  recommended  by  one  engineer 
that  instead  of  a  spade  a  hoe  be  used  with  the  blade  bent 
nearly  in  line  with  the  handle. 

Another  way  by  which  a  mortar  finish  may  be  made  is  to 
plaster  the  forms  with  cement  mortar  in  advance  of  plac- 
ing the  concrete.  The  mortar  and  concrete  are  united  by 
tamping. 

Another  way  to  obtain  a  mortar  finish  is  to  place  a  loose 
board  against  the  forms  and  tamp  the  concrete  behind  the 
board.  The  board  is  then  removed  and  mortar  run  into 
the  space  that  it  occupied.  This  is  of  course  only  appli- 
cable to  comparatively  dry  concrete. 

Still  another  method  is  to  use  a  sheet  of  steel  on  the 
one  side  of  which  are  riveted  i"  x  i"  angle  irons  to  act 
as  runners  and  spacers.  The  sheet  may  be  any  convenient 
width  and  length,  depending  on  the  nature  and  size  of  the 
work.  It  is  flared  out  at  the  upper  edge  to  act  as  a  hop- 
per. The  contrivance  is  placed  with  the  angle  irons  against 

96 


the  surface  to  receive  the  mortar  finish.  Mortar  is  placed 
on  one  side  and  concrete  on  the  other.  Then  by  means 
of  handles  the  sheet  is  drawn  up  and  the  concrete  tamped 
to  unite  the  mortar  and  concrete.  It  should  not  be  drawn 
quite  out  of  the  concrete.  There  is  difficulty  in  carry- 
ing up  a  long  line  of  this  kind  of  concreting,  especially  at 
corners  and  at  the  junction  of  two  sheets.  It  cannot  be 
worked  wrell  in  a  narrow  space. 

Of  the  foregoing  methods  the  manipulation  with  the 
spade  or  other  similar  tool  against  the  forms  is  probably 
the  most  satisfactory  for  the  reasons  that  it  can  be  done 
with  wet  concrete  and  in  a  narrow  space,  and  because  it 
results  in  a  more  uniform  concrete.  The  mortar  of  the 
entire  mass  is  uniform,  the  only  difference  at  the  sur- 
face being  that  the  stones  are  not  exposed.  Separate  mor- 
tars do  not  bond  so  well.  It  is  especially  true  of  work  done 
in  freezing  weather  that  a  mortar  of  a  different  mixture 
from  that  of  the  concrete  is  apt  to  break  away  from  the 
body. 

Concrete  of  small  aggregates,  as  that  used  in  reinforced 
concrete,  does  not  need  to  have  the  mortar  brought  to  the 
.surface,  as  a  rule.  The  churning  and  puddling,  which 
should  be  done  in  any  case  to  work  out  the  air  bubbles 
and  to  work  the  concrete  into  corners  and  around  the 
steel,  will  serve  to  give  the  concrete  the  smooth  surface 
desired,  if  the  mixture  is  the  proper  richness  and  con- 
sistency. 

In  order  to  cover  up  the  roughness  of  the  boards  and 
to  prevent  them  from  adhering  to  the  concrete,  as  well 
as  to  prevent  the  knots  from  discoloring  the  concrete,  a 
filling  coat  is  sometimes  used  on  the  wood.  Soft  soap 
may  be  used  for  this  purpose,  applied  with  a  brush.  Lin- 
seed oil  may  also  be  used.  Fatty  oils  should  not  be  used, 
as  they  act  on  fresh  concrete  disintegrating  and  discolor- 
ing it.  Hot  paraffine  is  sometimes  used.  Crude  oil  is  a 
very  good  substance  to  prevent  adhesion  of  the  concrete 
to  the  wood.  A  mixture  of  crude  oil  and  kerosene  also 
gives  good  results. 

97 


If  the  wood  is  thoroughly  wet  with  water  before  the 
concrete  is  laid,  there  is  not  much  danger  of  concrete  ad- 
hering. This  wetting  is  to  be  recommended  for  the  fur- 
ther reason  that  the  wood  will  not  then  absorb  water  from 
the  concrete. 

Paper,  unless  it  is  oiled,  will  stick  to  the  concrete  and  is 
hard  to  remove.  Burning  may  have  to  be  resorted  to. 

One  method  used  successfully  to  cover  up  the  grain  of 
the  wood  was  to  paint  the  surface  with  a  gloss  oil  and  to 
blow  sand  into  this  with  a  bellows. 

The  author  does  not  know  of  any  case  where  canvass 
painted  with  linseed  oil  has  been  used  as  a  cover  for  rough 
forms,  but  he  believes  it  would  be  an  admirable  material 
for  the  purpose.  It  is  waterproof  and  would  therefore 
not  absorb  water  from  the  concrete;  it  would  also  prevent 
the  leaking  of  the  liquid  mortar  that  occurs  at  cracks  or 
joints  in  the  wooden  forms.  It  would  probably  be  econom- 
ical for  the  reason  that  it  does  not  require  planed  boards 
in  the  forms  and  it  could  no  doubt  be  use'd  repeatedly. 
It  would  further  help  to  keep  the  frost  out  of  the  concrete. 

With  all  the  means  used  to  cover  up  the  irregularities 
of  the  wood  and  to  make  the  surface  smooth  there  will 
still  be  some  roughness  not  commercially  avoidable.  Some 
treatment  after  removal  of  the  forms  is  generally  neces- 
sary. Air  pockets  may  occur  in  places  where  the  holes 
will  be  exposed.  These  should  be  plastered  with  a  rich 
mortar.  Corners  may  break  off  in  removing  the  forms. 
These  should  also  be  plastered.  If  large  chunks  of  con- 
crete break  away  in  an  important  part  of  the  structure, 
the  best  thing  to  do  may  be  to  remold  the  piece.  Any 
sign  of  extended  weakness  in  the  concrete  may  show 
that  a  bad  batch  of  concrete  was  used  or  that  the  con- 
crete has  been  mistreated  during  setting. 

If  made  right,  the  concrete  surface  will  have  a  skin  of 
neat  cement.  It  is  generally  desirable  for  appearance  sake 
to  remove  this,  and  there  are  several  ways  to  do  it,  de- 
pending upon  the  length  of  time  that  the  concrete  has  set, 
before  it  can  be  made  accessible  for  treatment.  The  time 

a 


that  elapses  from  the  placing  of  the  concrete  until  the 
surface  can  be  exposed  depends  upon  the  kind  of  concrete 
and  the  nature  of  the  part  of  the  structure  in  question. 

If  the  surface  can  be  exposed  a  few  hours  after  the 
concrete  is  placed,  this  cement  may  be  removed  with  clean 
water  applied  by  means  of  a  hose.  The  hose  should  be 
used  without  a  nozzle,  as  the  pressure  would  gouge  out 
stones.  Water  may  also  be  applied  with  buckets.  Heavy 
walls  in  dry  concrete  could  probably  have  the  forms  re- 
moved in  half  a  day  or  so  after  concrete  is  placed,  and 
the  surface  could  be  thus  treated.  The  forms  should  not 
be  removed  so  soon  on  a  high  section  of  wall. 

If  the  concrete  has  set  for  about  24  hours,  clean  water 
and  scrubbing  brushes  will  remove  the  outside  skin  of 
cement.  If  about  two  days  have  elapsed,  wire  brushes 
may  be  needed,  using  water  to  wash  away  the  loosened 
cement.  If  the  concrete  surface  is  hard,  more  vigorous 
work  is  required  to  make  it  smooth  and  to  take  off  the 
skin  of  cement.  Blocks  of  sandstone,  or  of  concrete  of 
cement  and  sand,  or  of  carborundum,  with  water,  may  be 
used  to  scour  the  surface.  These  are  rubbed  with  a  cir- 
cular motion.  When  a  sand  blast  is  available,  this  is  an 
excellent  means  of  accomplishing  the  desired  result. 

Some  preliminary  treatment  will  usually  be  found  to 
be  necessary,  such  as  chipping  off  rough  projections,  as 
those  left  by  cracks  in  the  mold,  filing  off  the  arrises,  etc. 

These  scouring  processes  have  for  their  object  the  se- 
curing of  a  smooth  surface.  Sometimes,  after  the  surface 
is  washed  and  scoured  reasonably  smooth,  some  grout  of 
cement  and  sand  is  brushed  on,  and  by  the  same  circular 
motion  with  the  bricks,  this  grout  is  worked  into  any 
pores  in  the  surface.  The  result,  after  the  setting  of  the 
grout  is  a  very  smooth  surface. 

A  smooth  surface  is  not  always  desirable.  Some  rough- 
ness is  more  in  keeping  with  the  nature  of  the  concrete 
anH  is  more  pleasing  in  appearance  in  many  situations. 
The  washing  or  scrubbing  off  of  the  skin  of  neat  cement, 
above  described,  will  expose  the  surface  of  tfie  aggregate 

99 


and  leave  the  desirable  dull  or  rough  surface  without  any 
further  treatment.  The  appearance  will  then  depend  upon 
the  selection  of  the  aggregate.  If  a  mortar  of  sand  and 
cement  be  exposed  on  the  finished  surface,  the  washed 
surface  will  resemble  sandstone.  By  using  white  sand  the 
appearance  will  be  that  of  nearly  pure  white  sandstone. 
Other  colors  can  be  obtained  by  using  different  colored 
sands. 

Torpedo  sand,  a  sand  having  large  grains,  used  in  the 
surface  mortar,  will,  when  the  surface  is  washed  clean  of 
the  cement  skin,  give  a  good  appearance.  The  same  is 
true  of  small  regular  sized  pebbles  or  of  small  sized 
crushed  granite  or  limestone,  screened  to  */i  in.  or  so. 
Colored  granite  can  be  used  with  good  effect  to  obtain  a 
red,  black,  or  gray  surface.  Colors  obtained  in  this  way 
are  more  durable  and  uniform  than  those  made  by  use 
of  coloring  pigments. 

The  surface  treatment  by  use  of  regular  sized  particles 
in  the  aggregate  and  subsequent  washing  off  of  the  skin 
of  cement  may  be  carried  to  any  size  of  stones,  even  to* 
that  of  cobble  stones.  This  style  of  finish  in  pebble  size 
is  especially  appropriate  in  park  pavilions,  concrete  fences, 
etc.  If  a  dense  impervious  concrete  is  not  essential,  a 
dry  mixture  can  be  used  and  the  washing  away  of  the 
mortar  skin  dispensed  with.  This  sort  of  finish  on  rein- 
forced concrete  arches  can  be  employed  by  using  the  dry 
concrete  with  coarse  sand,  or  small  pebbles,  or  1A  in.  bro- 
ken stone  for  a  depth  of  an  inch  or  so  against  the  forms 
and  a  wet  impervious  concrete  surrounding  the  steel. 

Where  the  concrete  is  molded  and  not  plastered,  there 
is  an  advantage  in  using  a  stiff  mixture  in  preference  to  a 
wet  mixture,  as  the  forms  can  be  removed  in  a  shorter 
time,  and  the  washing  off  of  the  cement  is  easier  and 
cheaper  of  accomplishment  than  when  it  has  a  harder  set. 
The  lack  of  density  and  impermeability  due  to  the  dry 
mixture  would  make  this  method  less  applicable  to  build- 
ings whose  character  demands  that  the  walls  be  not  ab- 
sorbent of  water. 

100 


Concrete  of  materials  not  affected  by  acids,  such  as  sand, 
gravel,  granite,  and  trap  can  be  treated  to  a  surface  scrub- 
bing of  a  20  per  cent,  solution  of  hydrochloric  acid.  This 
will  remove  the  cement  skin,  even  after  a  hard  set.  The 
acid  must  be  immediately  neutralized  with  alkali  to  pre- 
vent penetration  into  the  concrete,  and  all  must  be  washed 
off  with  clean  water.  The  disadvantages  connected  with 
this  method  are  the  high  cost  and  the  difficulty  of  hand- 
ling the  acid  to  apply  it  and  the  fact  that  the  acid  that 
wastes  and  is  not  neutralized  may  penetrate  into  the  base 
of  the  structure  and  destroy  the  concrete. 

This  acid  wash  may  also  be  used  to  remove  efflorescence 
from  concrete  surfaces. 

Coloring  of  the  surface  of  concrete  may  be  effected,  as 
stated,  by  using  naturally  colored  aggregates  and  washing 
the  surface.  Pigments  are  also  used.  These  are  not  apt 
to  be  very  permanent.  If  used  in  large  quantities  they  will 
weaken  the  concrete.  If  used  in  the  entire  body  there  is 
a  waste  of  material  in  that  which  is  not  exposed,  and  it  is 
difficult  to  get  uniformity  by  any  other  means,  unless  it 
is  a  case  where  plastering  is  permissible.  If  pigments  are 
used,  it  is  best  to  mix  them  thoroughly  with  the  dry  ce- 
ment. A  little  lamp  black  can  be  used  to  advantage  in 
ordinary  concrete  to  relieve  the  dirty  color  of  the  concrete. 
This  could  be  placed  in  the  mixer  with  the  cement,  a  given 
quantity  for  each  bag  of  cement. 

Concrete  surfaces  will  not  hold  oil  paint  very  well;  the 
washing  off  of  the  skin  of  neat  cement  will  make  them 
more  retentive.  In  any  event  oil  paint  is  not  appropriate 
to  the  nature  of  the  concrete  except  for  interior  walls  and 
ceilings.  A  wash  of  neat  cement  can  be  applied  to  a  wall, 
or  the  cement  may  be  mixed  with  plaster  of  Paris  or  bet- 
ter with  marble  dust.  Either  of  the  latter  will  give  the 
appearance  of  marble.  In  applying  these  the  mixture 
should  not  be  too  thin  or  it  will  crock.  If  it  is  too  thick 
it  cannot  be  worked  with  the  brush.  An  ordinary  white- 
wash brush  is  used  in  its  application.  It  is  necessary  that 
the  surface  be  thoroughly  drenched  with  water  just  before 

101 


the  application,  otherwise  the  wall  will  absorb  the  water 
in  the  cement  and  prevent  setting.  The  surface  must  be 
kept  wet  for  a  day  or  so. 

Some  of  the  things  that  contribute  to  unsightly  appear- 
ance in  concrete  work  are  the  following.  Their  remedy 
is  evident,  (i)  Irregularity  in  the  nature  of  the  ingre- 
dients. This  applies  to  the  stone,  sand,  and  cement.  It  is 
evident  that  unless  the  first  two  run  uniform,  there  will  not 
be  a  uniform  surface  on  the  concrete.  It  is  also  true  that 
different  brands  of  cement  may  give  different  colors.  (2) 
Lack  of  uniformity  in  the  amounts  of  ingredients  in  each 
batch.  (3)  Insufficient  mixing  in  any  or  all  batches  of 
concrete.  (4)  Dirt  on  the  forms.  (5)  Want  of  care  in 
placing,  tamping,  spading,  etc. 

Of  surfaces  that  face  upward,  vertical  surfaces,  and 
those  that  face  downward  the  latter  are  the  most  difficult 
of  treatment.  This  is  of  course  because  of  the  fact  that 
generally  from  two  to  four  weeks  must  elapse  after  plac- 
ing the  concrete  before  these  can  be  safely  exposed,  because 
of  the  necessity  of  supporting  the  setting  concrete.  The 
difficulty  of  reaching  such  surfaces  makes  their  treatment 
doubly  expensive.  A  sandblast  or  scouring  with  bricks  for 
interior  exposed  beams  and  ceilings  would  be  best.  For- 
tunately in  arches  and  exterior  girder  work  the  under 
side  does  not  show  up  to  any  extent  and  can  often  be  left 
rough. 

Pavements  and  floors  are  in  a  class  by  themselves  and 
offer  the  most  satisfactory  conditions  for  surface  finish. 
Ordinary  sidewalks  as  commercially  made  are  often  put 
down  in  the  following  way.  After  the  sub-grade  is  tamped 
and  the  layer  of  cinders  or  broken  stone  for  drainage  is 
laid  down  and  tamped  (generally  a  thickness  of  4  to  6 
inches)  a  layer  of  stiff  concrete  is  placed  and  rammed. 
This  is  about  3  or  4  inches  thick  and  is  usually  a  gravel 
concrete  of  about  1 13 :6  mixture.  This  concrete  base  is 
blocked  off  and  sand  joints  used  to  separate  the  blocks. 
Then  this  concrete  is  left  until  the  next  day,  when  a  top 
coat  of  cement  mortar  is  laid,  usually  a  i  :2  or  1 13  mixture 

* 


of  cement  and  sand  or  crushed  granite  }i"  size  and  under. 
This  finishing  layer  is  generally  a  rather  stiff  mixture. 
When  placed,  it  is  troweled  smooth  and  cut  into  blocks, 
the  cuts  being  directly  over  the  sand  joints  in  the  concrete 
base  below.  After  hard  troweling  to  a  smooth  surface  a 
toothed  roller  is  passed  over  the  surface  to  give  it  a  some- 
what roughened  surface.  The  advantages  in  this  kind  of 
pavement  are  largely  on  the  contractor's  side.  He  does 
not  waste  any  cement  that  would  be  in  extra  mortar,  if 
wet  concrete  were  used,  and  some  of  it  should  flow  down 
into  the  base  of  loose  stone  used  for  drainage.  Without 
a  rich  top  coat  he  obtains  a  rich  skin  on  the  top  of  the 
pavement  by  troweling.  Why  the  pavement  is  allowed  to 
stand  a  day  before  the  top  coat  is  laid,  and  the  union  of 
the  top  coat  with  the  base  endangered,  is  not  clear. 

A  better  method  (and  the  method  employed  by  some 
pavers)  is  to  use  a  moderately  wet  concrete  and  to  place 
on  this  without  any  intermission  the  finish  coat  and  to  re- 
duce the  troweling  to  a  minimum.  Work  expended  on 
troweling  would  often  be  better  employed,  if  it  went  to- 
ward a  more  thorough  mixing  of  the  mortar.  If  the  mor- 
tar be  placed  on  the  fresh  concrete  before  the  latter  has 
time  to  take  on  an  initial  set,  a  good  bond  will  be  effected, 
and  in  no  other  way  can  such  bond  be  assured. 

Some  of  the  faults  that  are  very  common  in  sidewalks 
are  pitting  of  the  surface,  mapping  and  hair  cracks  or 
even  large  and  growing  cracks,  and  breaking  off  of  pieces 
down  to  the  concrete  base.  The  latter  sometimes  exhib- 
its itself  in  the  splitting  away  of  the  top  coat  from  the 
concrete  base,  and  the  pavement  has  a  hollow  sound. 

These  faults  are  largely  the  result  of  the  method  of  mak- 
ing pavements  above  described.  Excessive  troweling,  es- 
pecially in  a  mortar  not  rich  in  cement,  draws  to  the  sur- 
face a  skin  of  cement  and  leaves  just  below  it  sand  or 
screenings  partially  robbed  of  their  cement.  This  neat 
cement  does  not  possess  much  resistance  to  wear,  and  when 
it  is  worn  off  the  insufficiently  cemented  sand  or  screenings 
show  up  in  spots  or  pits.  Another  result  of  much  trowel- 
103 


ing  is  that  the  skin  of  cement  thus  formed  shrinks  in  set- 
ting and  causes  hair  cracks  or  mapping  of  the  surface. 
Sometimes  large  shrinkage  cracks  are  formed,  which  con- 
tinue to  increase  in  size.  Lack  of  proper  provision  for 
expansion  and  contraction  at  the  regular  joints  intended 
co  take  up  the  motion  may  be  the  cause  of  some  of  the 
large  cracks  observed.  It  is  not  enough  to  make  a  groove 
at  the  surface  of  the  pavement  to  relieve  the  tension.  There 
should  be  a  complete  separation  of  the  blocks. 

The  splitting  away  of  the  mortar  coat  is  the  natural  re- 
sult of  insufficient  bonding  between  the  concrete  base  and 
the  mortar  finish. 

In  contrast  with  the  method  of  laying  pavements  above 
referred  to  the  author  recently  observed  the  laying  of  con- 
crete in  the  floor  of  one  of  the  largest  reinforced  concrete 
buildings  in  the  world.  While  the  body  of  the  concrete 
was  fresh,  the  surface  being  quite  rough,  no  attempt  what- 
ever having  been  made  to  make  it  even  approximately 
horizontal,  the  mortar  for  the  top  finish  was  poured.  This 
was  of  the  consistency  of  soup.  Men  waded  in  concrete 
6  or  8  inches  deep  to  spread  the  mortar  about  with  shovels. 
Then  the  top  surface  was  leveled  off  by  working  a  straight 
edge  back  and  forth.  In  this  work  the  concrete  of  the 
body  of  the  floor  slabs  while  it  was  soft  enough  to  allow 
the  men's  feet  to  sink  into  it,  did  not  show  any  water  on 
the  surface  for  the  reason  that  it  was  not  tamped. 

If  there  is  an  excess  of  water  in  the  concrete  base  in 
pavement  work  the  bond  may  be  impaired  between  this 
and  the  finishing  mortar.  Concrete  in  the  base  almost  wet 
enough  to  flow,  spread  out  to  a  uniform  depth  with  rakes 
rather  than  tamped  to  a  smooth  flat  surface  covered  with 
laitance,  would  present  a  much  better  opportunity  for  the 
bonding  of  the  finishing  mortar. 

In  steps  and  other  parts  where  vertical  surfaces  must  be 
finished  off  it  is  necessary  in  the  ordinary  methods  of  mak- 
ing sidewalks,  to  use  stiff  concrete  and  to  plaster  on  the 
mortar,  also  a  stiff  mixture,  as  soon  as  the  molds  can  be 
removed.  The  necessity  for  using  stiff  concrete  is  to  allow 

104 


of  early  removal  of  the  molds,  so  that  plastering  can  be 
done  on  the  surface  before  the  concrete  has  a  hard  set. 
Generally  steps  are  troweled  to  a  smooth  finish,  though  the 
treads  would  be  better  to  have  a  rough  surface  to  prevent 
slipping. 

The  rough  surface  on  pavements,  so  desirable  on  steep 
grades  and  in  fact  desirable  most  anywhere  to  overcome 
slipperiness  in  cold  or  muddy  weather,  is  obtained  in  sev- 
eral ways.  A  steel  trowel  must  not  be  used  in  the  finish- 
ing process,  if  any  kind  of  rough  surface  is  to  be  made. 
In  fact  a  steel  trowel  should  be  used  sparingly  in  pave- 
ments. If  a  smooth  glossy  surface  is  wanted,  it  should  be 
made  by  using  a  rich  mixture  and  fine  sand  in  the  finish- 
ing mortar  rather  than  by  rubbing  with  a  steel  trowel. 

In  the  process  of  leveling  off  the  pavement  when  the 
mortar  coat  is  laid  a  wooden  straight  edge  is  used.  This 
is  worked  back  and  forth  on  the  side  boards  forming  the 
mold  for  the  pavement  until  all  of  the  high  places  are 
brought  down  and  all  of  the  hollow  places  filled  in.  If 
the  mortar  is  uniform  in  consistency  and  well  mixed,  the 
work  could  stop  here,  so  far  as  the  greater  part  of  the 
surface  is  concerned,  and  the  rounding  of  corners  and 
marking  and  dividing  into  blocks  would  complete  the  pave- 
ment. A  strip  about  iVz  in.  wide  rubbed  smooth  with 
a  tool  for  the  purpose  is  usually  made  around  each  block. 
The  surface  can  be  given  a  kind  of  regularity,  if  in  man- 
ipulating the  straight  edge  it  be  moved  back  and  forth  two 
or  three  inches  as  it  is  pushed  forward  making  sinuous 
lines  along  the  pavement.  A  wooden  float  may  be  used, 
after  the  surface  is  made  horizontal  by  the  straight  edge 
or  by  a  trowel,  where  a  straight  edge  cannot  be  employed. 
The  desired  roughness  can  be  made  in  this  way.  What 
is  probably  the  most  pleasing  surface  appearance  for  pave- 
ments is  obtained  by  use  of  a  wooden  plate.  The  surface 
is  stippled  with  this,  and  by  suction  against  it  a  most  work- 
manlike and  artistic  finish  results.  Another  way  to  pro- 
duce the  rough  surface  is  to  throw  the  last  half  inch  or 
so  of  mortar  with  the  trowel,  a  little  at  a  time. 

105  |j 


It  is  a  mistake  to  sprinkle  dry  cement  on  the  surface 
of  a  pavement. 

To  overcome  the  tension  due  to  troweling,  where  the 
pavement  is  troweled,  and  to  roughen  the  surface  it  may 
be  broomed  or  brushed  with  a  corn  brush  just  after  trow- 
eling. 

Where  a  smooth  troweled  surface  is  desired  the  final 
rubbing  should  be  done  a  half  an  hour  or  so  after  the 
mortar  is  laid.  Less  cement  would  then  be  drawn  to  the 
surface,  and  the  surface  tension  will  be  less.  For  smooth 
troweling  the  mixture  should  not  be  very  wet. 

It  is  best  to  lay  pavements  in  alternate  blocks  against 
bulkheads  or  vertical  boards  placed  temporarily  where  joints 
are  to  be.  Where  this  is  not  done,  the  concrete  base  should 
be  marked  off  in  blocks  and  separated,  while  the  concrete 
is  green,  by  making  joints  ^4  inch  wide  or  so,  filled  with 
sand  or  tar  paper  or  other  filler.  The  location  of  these 
must  be  marked  before  the  mortar  finish  is  laid,  and  when 
the  latter  is  finished  oft"  it  should  be  cut  with  a  thin  trowel 
making  a  complete  separation  and  not  merely  a  groove. 
Very  little  if  any  space  is  needed  between  blocks  to  take 
up  expansion  and  contraction  due  to  change  in  tempera- 
ture, but  the  contraction  due  to  shrinkage  in  setting  may 
be  enough  to  split  the  block  at  some  other  section  than 
in  the  groove,  unless  a  complete  separation  is  made. 

Pavements  that  are  not  on  a  grade  are  generally  given 
a  slope  of  ^4  in.  to  the  foot  for  drainage. 

There  is  a  difference  of  opinion  as  to  the  proper  mix- 
ture for  a  mortar  finish  on  pavements.  Some  engineers 
would  not  use  a  mortar  richer  than  1 :2  or  1 :3  because  of 
the  fact  that  with  troweling  a  rich  mortar  will  check. 
Others  specify  mortar  coats  as  rich  as  1:1.  If  the  mortar 
is  of  the  same  richness  as  that  used  in  the  concrete  (e.  g. 
a  1 :2  mortar  for  a  1 12:4  concrete)  there  ought  to  be  equi- 
librium in  the  mass.  Mixtures  of  1:1%  to  1:2%  with 
granite  screenings  that  will  pass  through  a  sieve  having 
V*  in.  meshes  give  satisfactory  results.  The  former  is 
much  used  in  high  class  pavement  work.  Particularly 
106 


glossy  surfaces  are  obtained  by  richer  mixtures,  using  as 
rich  as  I  :i.  Such  pavements,  while  they  may  be  good  in 
the  interior  of  buildings,  are  too  slippery  for  out-of-doors. 

For  hard  smooth  surfaces  fine  sand  may  be  used.  Fine 
sand  should  only  be  used  in  a  rich  mixture.  For  a  rough 
surface  or  in  leaner  mixtures  use  coarse  sand  or  screen- 
ings. 

Plastering  on  vertical  surfaces  of  concrete  should  be 
avoided  where  practicable.  It  is  often  necessary,  however, 
and  when  it  is  done,  special  precautions  should  be  taken 
to  make  the  plaster  adhere.  If  it  is  not  important  that  the 
body  of  the  wall  be  dense  and  impermeable,  plastering 
will  adhere  better,  if  the  concrete  be  made  dry,  on  account 
of  the  rough  surface.  There  is  a  further  advantage  in 
using  dry  concrete,  if  other  considerations  do  not  demand 
wet  concrete,  namely;  the  forms  can  be  removed  soon 
after  the  concrete  is  placed  and  before  the  cement  has  a 
hard  set.  It  would  be  well  in  some  cases  to  wash  or  scrub 
the  surface  or  to  pick  it  before  applying  the  plaster.  Lime 
paste  mixed  with  the  cement  and  sand  for  plastering  in- 
creases the  adhesion  and  lessens  the  tendency  for  hair 
cracks  to  form  on  the  surface.  Lime  delays  the  setting  of 
the  cement  and  makes  it  easier  to  work.  Lime  paste  can  be 
used  in  quantities  up  to  an  equal  amount  with  the  cement. 
If  a  hard  surface  is  desired,  less  lime  would  be  used.  In 
this  plastering,  as  in  pavements,  it  is  well  to  go  over  the 
surface  with  a  brush  or  broom  after  troweling  to  relieve 
the  tension  of  the  cement.  In  plastering  piers  and  abut- 
ments the  trowel  marks  can  be  removed  by  brushing  hori- 
zontally with  a  whisk  broom.  The  surface  appearance  is 
greatly  improved  by  this  means. 

A  simple,  and  inexpensive  mode  of  plastering  is  what 
is  called  a  splatterdash  coat.  The  mortar  is  thrown  or 
splashed  against  the  surface  with  a  paddle.  An  effective 
rough  surface  can  be  made  in  this  way.  The  methods 
used  on  pavements  to  produce  a  rough  surface,  by  means 
of  wooden  floats  and  stippling,  can  be  employed  to  good 
advantage  on  walls.  A  rough  surface  is  generally  better  in 
107 


appearance  and  less  liable  to  crack  than  a  smooth  surface. 

A  method  recommended  to  secure  a  good  bond  is  as  fol- 
lows. First  the  surface  is  washed,  then  after  thorough 
drenching  with  water  a  coat  of  neat  cement  grout  is  brush- 
ed on.  While  this  is  still  wet  a  coat  of  plaster  about  % 
in.  thick  is  put  on.  Succeeding  coats  of  the  same  thick- 
ness are  applied  about  an  hour  apart  until  the  desired 
thickness  is  attained.  As  a  finish  the  last  mortar  may  be 
thrown  on,  to  give  a  rough  surface. 

Plastering  should,  in  general,  be  resorted  to  only  to  fill 
in  holes  and  to  smooth  over  rough  places.  A  plaster  coat 
should  either  be  very  thin,  that  is,  just  enough  to  fill  ir- 
regularities, or  it  should  be  one  to  three  inches  thick,  so 
that  it  will  have  some  strength  in  itself. 

In  making  steps  the  forms  should  be  of  planed  boards. 
The  mortar  of  the  concrete  should  be  worked  up  against 
the  forms  in  a  manner  heretofore  described.  Upon  re- 
moval of  the  forms  the  surface  can  be  made  smooth  by 
plastering  up  any  holes  with  a  I  :i  or  1 :2  mortar  and  by 
using  the  same  in  a  wash  over  the  surface,  rubbing  it 
smooth  with  a  wooden  float  or  with  a  scouring  brick. 

In  sea  walls  it  is  well  to  have  as  smooth  and  dense  a 
surface  as  possible.  This  is  to  prevent  penetration  of  the 
salts. 

It  is  said  that  mortar  that  has  set  up  for  3  or  4  hours 
will  adhere  better  as  a  plaster  and  shrink  less  than  fresh- 
ly mixed  mortar. 

On  a  dry,  hard  surface  a  plaster  coat  or  floor  finish 
should  be  2  or  3  inches  thick. 

On  a  brick  wall  or  on  cinder  concrete  nails  can  be  driv- 
en in  to  anchor  the  plaster,  or  expanded  metal  or  other 
metal  lath  can  be  nailed  on  and  plastering  done  on  this 
base.  Old  brick  buildings  can  by  this  means  be  given  a 
cement  finish,  which,  when  properly  done,  enhances  their 
appearance  very  greatly. 

Old  wooden  floors  can  be  covered  with  a  finish  of  % 
in.  or  more  of  a  concrete  made  with  saw  dust  as  one  of 
the  aggregates.  This,  too,  is  anchored  to  the  floor  by 

108 


means  of  nails  driven  into  the  wood.  The  use  of  this  kind 
of  floor  finish  on  new  concrete  floors  has  not  received  the 
attention  and  trial  it  deserves,  possibly  on  account  of  the 
lack  of  workmen  skilled  in  its  manipulation. 

Common  sense  and  artistic  judgment  are  probably  vio- 
lated more  in  the  matter  of  the  finish  for  cast  blocks  than 
in  any  other  line.  There  are  probably  more  "rock  face" 
blocks  made  than  any  other  kind,  and  there  is  nothing  more 
absurd  than  an  imitation  of  rock  faced  stone  blocks  in  cast 
stone  work.  Cast  stone  or  concrete  blocks  can  never  have 
any  standing  so  long  as  their  very  appearance  holds  them 
out  to  be  what  they  are  not.  It  is  legitimate  to  tool  dress  or 
finish  concrete  blocks  or  artificial  stone,  but  it  is  not  legiti- 
mate to  cast  in  them  an  imitation  of  a  dressing  which  they 
do  not  receive.  Rock  faced  is  the  name  given  to  the  finish 
of  stone  that  has  been  rough  dressed.  The  surface  is  the  nat- 
ural fracture  of  the  stone.  No  mason  would  attempt  to  pro- 
duce this  appearance  by  carving  the  entire  surface.  It 
would  not  be  economical  in  concrete  blocks  to  break  off 
enough  of  the  surface  to  produce  this  effect,  even  if  the 
concrete  should  possess  the  property  of  fracturing  in  this 
way.  Its  sole  beauty  lies  in  its  irregularity  and  in  the  fact 
that  it  is  a  natural  and  not  an  artificial  result.  In  con- 
crete blocks  regularity  is  necessary  and  painfully  manifest. 
It  would  be  as  rational  to  carve  a  human  face  in  the  rugged 
side  of  a  mountain  of  rock  to  enhance  its  beauty  as  it  is 
to  cast  a  rugged  face  in  a  molded  block. 

A  very  satisfactory  surface  is  obtained  in  concrete  by 
tooling.  For  rough  work  a  pick  may  be  used  to  break  off 
the  outer  skin.  Light  picks  may  be  employed  on  the  sur- 
face while  the  concrete  is  rather  green.  A  cheap  and  effec- 
tive finish  can  be  obtained  in  this  way.  This  is  especially 
suitable  for  factory  buildings.  The  picking  is  done,  light- 
ly, and  it  is  said  that  a  workman  can  finish  1,000  sq.  ft. 
a  day.  A  pointed  chisel  may  be  used  for  the  surface  of 
heavy  walls.  Smaller  work  may  be  crandalled.  Bush  ham- 
mering is  another  method  employed;  this  may  be  done  by 
an  unskilled  workman.  To  avoid  a  broad  expanse  of  flat 
109 


surface  the  wall  should  be  laid  off  in  panels.  A  good  way 
is  to  divide  the  surface  into  blocks  by  nailing  triangular 
strips  on  the  forms.  The  V  shaped  grooves  would  not  be 
dressed,  but  only  the  flat.  part. 

For  chisel  dressing  allow  }4  to  %  in.  to  be  removed  by 
the  tool.  Bush  hammering  on  a  good  flat  surface  need  not 
cut  in  any  measurable  depth.  All  arrises  should  be  round- 
ed to  about  %  in.  radius.  A  file  can  be  used  for  this  pur- 
pose. Dressing  with  hammers  should  not  be  done  before 
the  concrete  is  a  month  or  two  old.  Small  stones  are  apt 
to  be  dislodged  by  the  process,  unless  they  are  firmly  ce- 
mented in. 

On  some  kinds  of  artificial  building  stones  a  tooling  ma- 
chine of  carborundum  wheels  is  used.  This  can  be  used 
on  very  green  concrete,  as  it  grinds  soft  and  hard  spots 
alike  and  does  not  jar  the  stone.  The  surface  finish  is  very 
good. 

Where  compressed  air  is  available,  pneumatic  tools  for 
crandalling  or  otherwise  dressing  the  concrete  surface 
would  be  economical  and  satisfactory. 

It  may  be  found  difficult  to  dress  the  surface  of  a  con- 
crete made  of  a  hard  gravel.  The  stones  may  be  gouged 
out  of  the  cement  before  they  will  break. 

WLhedJettftCT-riol  . 

Forms  for  Concrete  Work. 

..Forms  should  be  designed  so  that  they  will  retain  their 
shape,  until  the  concrete  has  hardened  sufficiently  to  be  self 
supporting.  Hemlock  should  not  be  used,  except  in  the 
roughest  kind  of  work.  Spruce  and  pine  are  preferable. 
Kiln  dried  lumber  or  thoroughly  seasoned  lumber  is  not  de- 
sirable, because  the  dry  wood  will  swell.  Green  wood  is 
also  undesirable  on  account  of  liability  to  check  and  warp. 
Partly  seasoned  lumber  is  best. 

Whether  or  not  lumber  should  be  planed  will  be  deter- 
mined by  the  kind  of  surface  desired.     Dry  concrete  does 
not  require  tight  forms,  since  there  will  be  no  liquid  mor- 
110 


tar  to  run  out  of  the  cracks.  For  wet  concrete  the  forms 
should  be  as  tight  as  possible.  Cracks  may  be  filled,  where 
necessary,  with  putty  or  clay  or  plaster  of  Paris.  In  order 
to  prevent  excessive  pressure  and  heaving  of  forms  due 
to  swelling  the  boards  can  be  planed  beveled  on  one  edge, 
the  full  width  being  against  the  concrete.  The  narrow  edge 
of  a  board  will  then  be  brought  in  contact  with  the  wide 
edge  of  the  next.  Closer  fit  can  also  be  secured. 

For  fine  work  it  would  be  well  to  shellac  the  wood  to 
prevent  penetration  of  water  and  consequent  swelling.  If 
end  grain  is  in  contact  with  concrete,  it  should  be  covered 
with  shellac  to  prevent  absorption  of  water. 

Tongued  and  grooved  boards  are  best  for  a  smooth  sur- 
face, though  they  are  more  expensive.  Boards  surfaced 
on  one  side  and  on  the  edges  are  good  enough  for  most 
work. 

The  thickness  of  boards  used  for  sheathing  or  lagging 
should  be  such  as  to  keep  deflection  within  limits.  The 
thickness  will  be  determined  more  by  the  amount  of  deflec- 
tion than  by  the  extreme  fibre  stress  produced  by  the  load. 
In  general,  to  avoid  springing,  I  in.  boards  should  not  be 
used  on  wider  spacing  than  2  ft.  between  studding.  The 
span  for  i^  in.  plank  should  be  not  more  than  3  ft.  and 
that  for  2  in.  plank  not  more  than  4  ft.  for  vertical  loading. 
Wider  spacing  than  this  can  be  used,  where  the  pressure  is 
lateral,  as  in  walls  up  to  about  4  ft.  for  iVz  in.  plank  and 
6  ft.  for  2  in.  plank. 

For  the  under  side  of  floor  slabs  generally  one  inch 
boards  are  used,  with  studding  16  to  24  in.  apart.  For  col- 
umns and  the  sides  of  beams  one  inch  boards  may  also  be 
used  running  lengthwise  and  held  in  place  by  outside  forms 
made  of  2  in.  x  4  in.  or  larger  sized  pieces.  These  may 
be  spaced  at  intervals  of  about  two  ft.  and  held  in  place 
by  means  of  bolts  in  the  case  of  columns  or  be  wedged 
against  those  of  the  next  beam  in  the  case  of  beams.  A 
heavy  plank  along  the  bottom  of  a  beam  would  serve  to 
support  the  weight  on  the  shores  and  allow  the  removal 
of  the  side  sheathing  in  advance  of  the  bottom  supports. 
Hi 


Nailing  should  be  reduced  to  a  minimum,  as  the  jar  in 
knocking  off  the  forms,  if  nailed,  is  injurious  to  the  con- 
crete, also  the  wood  will  be  rendered  unfit  for  continued 
use  by  repeated  nailing.  Bolts  and  wedges  should  be  used 
where  possible  to  hold  the  studding  in  place. 

Thick  plank  will  be  found  more  economical  than  thin 
boards,  if  used  many  times,  as  they  will  hold  their  shape 
better  and  last  longer.  In  sewer,  culvert,  and  arch  work 
thick  lagging,  say  2  in.  plank  is  generally  used. 

Cutting  of  the  wood  should  be  avoided  as  much  as  pos- 
sible. 

Where  there  is  much  duplicate  work,  great  saving  can  be 
effected  by  making  the  forms  in  such  way  that  as  large 
sections  as  can  be  conveniently  handled  can  be  made  up 
into  units.  These  units  will  consist  of  frames,  say  of  2 
in.  x  4  in.  pieces,  to  which  the  boards  are  nailed,  the  frame 
to  be  rigid  enough  not  to  warp  in  handling.  In  high  walls 
these  units  are  very  useful.  In  a  retaining  wall,  for  ex- 
ample, if  one  side  only  of  the  wall  has  studding,  the  other 
side  may  be  brought  up  by  use  of  these  units.  If  two 
sets  are  employed  the  wrork  can  proceed  as  follows.  First, 
one  set  is  placed  in  position,  being  blocked  the  proper  dis- 
tance from  the  back  sheathing  of  the  wall  and  held  there- 
to by  means  of  bolts  passing  through  or  by  means  of  wires 
drawn  up  taut  by  twisting.  Then,  when  the  concrete  is 
nearly  up  to  the  top  of  this  row  of  frames,  another  row 
is  placed  above  in  the  same  manner.  When  the  space  thus 
formed  is  filled,  the  concrete  below  will  probably  be  self 
supporting.  The  first  row  of  units  can  then  be  removed 
and  placed  above  the  second,  and  so  on.  In  the  same  way 
the  forms  of  a  chimney  or  tank  can  be  made  in  segmental 
units  for  both  inside  and  outside.  With  two  or  more  sets 
of  these,  say  3  or  4  ft.  in  depth,  the  work  can  proceed  con- 
tinuously. One  set  only  of  the  units  requires  guides  or 
bracing  to  bring  and  hold  them  to  line.  It  is  generally 
best  to  brace  the  inside. 

Forms  for  floor  slabs  may  also  be  made  in  units,  say 
2  or  4  pieces  to  a  panel,  or  more  pieces  if  the  panels  are 
112 


large.  Designing  the  floor  so  that  the  panels  are  uniform 
in  size  will  greatly  facilitate  the  construction. 

Beams  and  girders  should  be  given  a  small  camber,  say 
an  inch  for  every  20  ft.  of  span. 

Wires  are  very  often  used  to  hold  forms  against  spread- 
ing. These  can  be  cut  off  with  cutting  pliers  at  the  sur- 
face of  the  concrete,  or,  to  prevent  rust  stains,  they  may 
be  cut  with  a  chisel  below  the  surface  and  the  hole  plas- 
tered up.  Bolts  are  sometimes  used  for  the  same  purpose 
and  removed  with  the  forms.  To  prevent  adhesion  to  the 
concrete  these  may  be  run  through  gas  pipe  or  tin  tubes, 
which  remain  in  the  concrete.  If  the  gas  pipe  or  tin  tube 
is  brought  out  nearly  to  the  surface  and  the  end  stuffed 
with  cloth  or  waste  to  prevent  admission  of  concrete,  thr 
bolt  may  be  drawn  out.  The  waste  packing  can  be  re- 
moved and  the  hole  plastered  up. 

Wooden  blocks  used  as  spacers  must  be  removed  as  con- 
crete is  placed.  No  wood  should  be  left  in  concrete,  either 
by  accident  or  for  any  structural  reason.  Wood  buried 
in  concrete  will  suffer  dry  rot,  as  it  cannot  season. 

Tie  rods  or  bolts  should  not  be  close  to  the  edge  of  the 
concrete,  as  they  are  liable  to  break  out  pieces  of  con- 
crete in  removing. 

In  sewer  work  for  sewers  of  sufficient  diameter  for  men 
to  work  in,  it  is  a  good  plan,  as  stated  elsewhere,  to  omit 
lagging  on  the  invert  up  to  a  point  where  it  is  needed  to 
prevent  flowing  of  concrete.  This  affords  better  oppor- 
tunity to  place  and  compact  the  concrete  as  well  as  to 
trowel  the  surface  to  a  smooth  finish.  The  ribs  would  be 
in  place  just  the  same  to  guide  in  forming  the  sewer. 
Loose  lagging  can  be  used  on  the  upper  part  of  the  sewer. 
This  allows  easy  removal  as  the  work  advances.  Loose 
lagging  on  culverts  and  arches  is  often  desirable. 

Vertical  props  should,  in  general,  be  braced  together. 
This  prevents  accidental  dislodgement  and  prevents  sway- 
ing of  the  structure.  The  props  or  shores  should  rest  on 
solid  footings  and  should  be  so  designed  that  they  can  be 
the  last  pieces  removed  and  that  they  can  be  left  in  place 
113 


even  after  the  concrete  is  self  supporting.  Such  a  condi- 
tion is  often  desirable  in  a  building  where  a  floor  is  support- 
ed by  props  to  a  floor  below,  the  latter  being  just  capable  of 
self  support.  It  may  be  necessary  to  allow  the  shores  to 
remain  in  the  successive  stories  down  to  the  foundation, 
in  order  not  to  strain  these  floors  with  load  they  are  not 
designed  to  carry,  until  the  top  floor  is  self  supporting. 
There  should  be  props  under  the  girders  close  to  columns 
so  as  to  relieve  the  green  concrete  of  the  columns  of  the 
weight  of  the  floors. 

Props  should  have  double  wedges  of  hard  wood  under 
them,  so  that  they  can  be  removed  without  jarring  the 
concrete  and  so  that  they  can  be  eased  off  without  removal, 
in  case  it  is  not  positively  known  that  the  concrete  is  thor- 
oughly hardened.  Very  heavy  posts  as  those  supporting 
long  span  arches  could  rest  in  sand  boxes  arranged  with 
gates  to  let  out  the  sand  and  lower  the  posts  by  this  means. 
For  a  unit  compression  on  posts  1,000  Ibs.  per  sq.  in. 
is  recommended  for  pieces  whose  unsupported  length  is 
ten  times  the  least  width  or  less,  and  400  Ibs.  per  sq.  in. 
for  pieces  whose  unsupported  length  is  forty  times  the 
least  width.  For  other  ratios  proportionate  values  are  to 
be  used.  Lengths  more  than  40  times  the  least  width 
should  be  avoided. 

For  beams  a  unit  of  800  Ibs.  per  sq.  in.  is  recommended. 

If  the  span  in  feet  be  divided  into  the  coefficient  C,  in  the 

following  list  of  common  sizes,  the  result  is  the  total  weight 

in  pounds  that  the  beam  will  carry  as  a  uniformly  distribut- 

•  ed  load. 

2  x     4,   €=2840 

2  x    5, C=  4440 

2  x    6, C=  6400 

2  x    8,   C=i  1400 

2  x    9,    0=14400 

2  x  10,    0=17800 

2   X    12, C=25600 

3x14,  0=52270 


114 


3x15, 
4  x  16, 

As  an  example,  suppose  it  is  desired  to  know  the  size 
of  joists  required  to  carry  a  6  in.  slab  of  concrete  on  joists 
spaced  18  in.  apart,  the  span  being  10  ft.  and  an  accidental 
load  of  75  Ibs.  per  sq.  ft.  being  provided  for.  The  total 
load  carried  by  a  joist  is  (75  +  75  or  150)  x  10  x  1.5  — 
2250  Ibs.  Reversing  the  rule  above  given  and  multiplying 
this  by  the  span  length  we  have  C  ~  22500.  Hence  2  x  12 
joists  would  be  needed. 

The  depth  of  beams  should  generally  be  between  one- 
tenth  and  one-twentieth  of  the  span.  Beams  deeper  than 
one-tenth  will  be  overstressed  in  shear,  when  strained  to 
their  capacity  in  bending;  beams  shallower  than  about 
one-twentieth  will  deflect  too  much  under  load. 

In  proportioning  the  forms  allowance  should  be  made 
for  accidental  load  that  may  be  placed  upon  the  floors  in 
the  processes  of  construction.  A  uniform  load  of  75  Ibs. 
per  sq.  ft.  for  slabs  and  of  50  Ibs.  per  sq.  ft.  for  beams  and 
girders  ought  to  cover  this  contingency,  as  well  as  the 
weight  of  forms,  except  where  the  forms  are  unusually 
heavy. 

The  lateral  pressure  of  the  green  concrete  may  be  taken 
as  equal  to  that  of  water,  keeping  in  view  the  amount  of 
concrete  that  will  be  placed  at  one  time. 

There  should  be  a  door  at  the  bottom  of  column  forms 
to  allow  cleaning  out  before  concrete  is  placed.  Also  the 
bottom  board  in  wall  forms  and  girder  forms  should  be 
placed  last  where  practicable. 

Collapsible  forms  for  tunnels,  culverts,  and  sewers  are 
often  made  use  of.  Sheet  steel  is  sometimes  used  in  place 
of  lagging  of  wood.  Forms  that  are  not  collapsible  may 
often  be  removed  by  revolving  about  the  vertical  axis; 
then  if  the  lagging  is  loose  and  not  nailed,  the  form  can 
readily  be  removed  and  placed  forward. 

A  good  and  economical  form  for  circular  columns  can 
be  made  of  sheet  steel.     It  may  be  made  of  two  semicircu- 
lar sections,  flanged  and  bolted  together. 
115 


In  bracing  forms  wooden  pieces  should  be  used,  generally 
2x4  scantling.  Wire  ropes  should  not  be  employed  for 
this  purpose  in  any  case,  as  the  stretch  in  these  may  be 
disastrous  to  the  structure. 

In  heavily  battered  walls,  as  the  wing  walls  for  an  abut- 
ment, a  cover  on  the  sloping  part  of  the  wall  is  generally 
necessary.  This  should  be  removed  as  soon  as  possible 
so  that  the  top  surface  can  be  plastered  and  made  inper- 
vious.  If  much  wet  concrete  is  poured  at  a  time  in  such 
wall,  it  may  be  necessary  to  tie  down  the  cover  of  the  slop- 
ing portion  to  prevent  its  being  lifted  by  the  pressure  of 
the  concrete.  It  could  be  anchored  by  wires  into  the  body 
of  the  wall.  If  secured  only  to  the  side  forms,  the  pres- 
sure might  lift  these. 

In  footings  and  retaining  walls,  instead  of  having  a  heavy 
batter,  steps  are  usually  preferable,  with  the  tread  sloped 
so  as  to  shed  water.  This  is  especially  true  when  dry  con- 
crete is  used,  as  it  allows  access  to  the  concrete  for  tamp- 
ing. 

Lateral  pressure  of  wet  or  of  tamped  concrete  must  not 
be  overlooked  in  the  building  and  bracing  of  forms.  The 
sides  of  beam  and  wall  forms  should  be  held  against  spring- 
ing by  bolts  and  wedges,  where  practicable,  or  by  stiff 
braces. 

A  suggested  scheme  for  slab  and  beam  forms  is  as  fol- 
lows. Use  a  heavy  plank  under  the  girder  4  in.  wider  than 
the  girder.  On  top  of  this  nail  a  one  inch  planed  board, 
the  width  of  the  girder,  along  the  middle  of  the  plank. 
There  will  be  a  2  in.  margin  on  each  side.  One  inch  of  this 
will  be  taken  up  with  the  side  boards  for  the  girder.  The 
other  inch  will  be  used  as  a  ledge  to  support  the  joists  for 
the  slab  which  can  be  blocked  up  by  nailing  them  to  the 
vertical  studding  for  the  sides  of  the  girder.  If  strips  be 
nailed  lightly  to  these  joists  and  studding,  and  if  the 
sheathing  for  slabs  and  girders  be  nailed  together  with 
cleats  to  form  units,  there  will  need  to  be  but  little  nail- 
ing into  the  wood  in  contact  with  the  concrete.  The  heavy 
plank  under  the  girder  should  be  supported  by  props  3 

116 


to  6  ft.  apart.  For  heavy  girders  it  may  be  stiffened  by 
knee  braces  to  the  props  or  by  a  pair  of  joists  nailed  to  the 
side  of  the  props.  By  the  above  described  arrangement 
the  forms  under  the  slabs  and  on  the  sides  of  girders  may 
fte  removed  and  used  elsewhere  while  the  weight  of  the 
girders  is  still  on  the  shores. 

It  is  important  that  columns  be  plumb  and  that  beams 
be  straight  and  true  to  line.  Before  beginning  to  place  the 
concrete  all  forms  should  be  brought  to  correct  position 
and  true  to  line  and  securely  braced.  Warped  and  inclined 
surfaces  of  walls,  intended  to  be  plane  and  vertical,  and 
wavy  copings  are  very  unsightly. 

Sharp  corners  in  the  concrete  should  be  avoided.  The 
arrises  should  generally  be  either  chamfered  off  in  the 
mold  or  trimmed  rounding  when  the  forms  are  removed. 

In  dividing  a  wall  into  blocks  the  joints  should  be  V 
shaped,  either  sharp  or  truncated.  The  recess  should  not 
have  parallel  sides,  as  the  withdrawing  of  the  molding 
pieces  would  break  off  spalls  of  concrete;  also  the  con- 
crete will  not  as  readily  fill  in,  around  the  squared  recess. 
The  same  is  true  of  moldings.  These  should  not  have  re- 
cesses with  parallel  sides.  Surfaces  that  face  upward 
should  in  general,  have  a  slope  outward  so  as  not  to  bind 
on  the  forms  and  so  as  to  allow  concrete  to  be  more  easily 
worked  under  the  form.  Further,  such  surfaces  will  turn 
the  water  and  absorb  less. 

The  design  of  the  work  should  be  made  with  a  view  of 
reducing  to  a  minimum  the  difficulties  inherent  in  the  hand- 
ling and  placing  of  concrete  and  with  an  appreciation  of 
the  skill  of  the  workmen  executing  the  plans.  Moldings 
should  be  as  simple  as  possible  and  in  conformity  with  the 
construction.  Small  arches  and  buildings  should  have 
light  moldings  and  ballustrades,  where  any  are  used.  Mas- 
sive structures  should  have  bold  and  massive  ornamen- 
tation. Fine  details  should  not  be  attempted  on  out-door 
work.  These  can  be  executed  by  use  of  lime  or  plaster  of 
Paris  in  conjunction  with  cement  for  indoor  ornamenta- 
tion. Imitations  should  be  avoided.  Broad  plain  surfaces 
117 


should  be  broken   up  by  paneling  where  practicable;  the 
heavier  the  work  the  more  massive  and  bold  the  paneling 

should  be. 

• 


The  Properties  of  Concrete 


Concrete  partakes  of  the  properties  of  the  stone  or  other 
aggregate  from  which  it  is  made,  though  these  properties 
are  affected  by  the  mortar  with  which  the  aggregate  is  ce- 
mented together.  The  property  of  greatest  importance  is 
the  compressive  strength.  The  compressive  strength  of  the 
concrete  is  in  general  less  than  that  of  the  stone  of  the 
aggregate.  The  unit  compressive  strength  tested  in  cubes 
is  generally  less  for  small  cubes  than  for  large  ones.  It 
is  greater  for  flat  discs  than  for  cubes,  the  flatter  the  disc 
the  higher  the  unit. 

On  account  of  the  many  factors  that  enter  in  the  manu- 
facture of  concrete  affecting  its  uniformity,  and  on  account 
of  the  very  nature  of  concrete,  being  a  non-homogeneous 
substance,  laws  that  are  even  approximately  exact  cannot 
be  written  that  will  tell  the  compressive  strength  without 
allowance  for  a  liberal  variation.  If  the  dimensions  of  the 
specimen  were  greatly  in  excess  of  the  largest  piece  of  the 
aggregate,  unit  results  would  no  doubt  be  more  uniform. 
Sand  and  cement  in  ordinary  sized  specimens  give  more 
uniform  units  than  concrete,  because  the  grain  of  sand 
bears  so  small  a  ratio  to  the  size  of  the  specimen  that  it  is 
possible  to  test. 

The  best  that  can  be  done  in  the  matter  of  establishing 
a  unit  value  for  concrete  in  compression  is  to  take  average 
values  of  a  large  number  of  tests  made  under  different 
conditions,  and  in  design  to  use  a  liberal  factor  of  safety 
to  cover  irregularities  and  imperfect  work.  A  standard 
concrete  should  be  used  in  reinforced  concrete,  and  uni- 
form conditions  should  be  striven  for.  The  cube  is  prob- 
ably the  best  standard  for  compressive  strength,  and  its 
size  should  be  from  8  to  12  in.  so  as  to  minimize  the 
effect  of  non- uniformity. 

118 


TESTS  &//  COMCRITZ  CUBES 

Aggregate  as  stated  /n  /$t  Co/umn. 

Compress/ve  Strength  in  /As  per  5q.  fnch  . 

I.  MORTAR-  /PORTLAND  CEMENT  :  /  SAND 

35 

x3§ 

| 

Kind 

Age 

1 

Average 

I 

of 

of 

3 

Compr 

Authority 

1 

Stone 

Cube 

^ 

Strength 

5 

^ 

/i 

Trap 

//  fo43dd. 

4 

3944 

U.  5.  /G9S 

3 

» 

7  »  //    . 

9 

2442 

»>                   9f 

3 

99 

19  "  26   " 

9 

3346 

99                t9 

3 

>-> 

31  »,48>  „ 

10 

3676 

9                    99 

3 

99 

61  »  76  99 

7 

45  9  / 

•>                    99 

3 

99 

4-  mo. 

6 

3079 

99 

3 

Pebbles 

7  to  //da 

4 

2092 

9> 

3 

99 

21  »26  " 

4 

3052 

9               99 

3 

19 

29  "46  99 

5 

3642 

9               99 

3 

»* 

61   »70  99 

3 

3793 

9 

3 

Cinder 

29  »39  99 

IQ 

1544 

3 

99 

9O  99/02  •» 

/5 

2/86 

3 

2  Trap  J  Grave/ 

Tbfr 

/ 

/80O 

3 

99                  99 

23  » 

/ 

3806 

9 

3 

99                  99 

32  » 

/ 

5O24 

3 

99                   99 

67  -» 

1 

4700 

3 

2  Pebbles  J6ra. 

7  » 

/ 

I486 

3 

99                   ->9 

22     99 

/ 

2676 

3 

99                   99 

32      99 

/ 

3000 

3 

99                      I) 

65      99 

1 

3800 

3 

1  Trap  j  Pebbles 
!  Gravel 

7  •>-> 

1 

/52O 

99               99 

3 

iTrapJfebbks 
1  6  ravel 

22  » 

1 

2800 

99             99 

3 

iTrep./fkbb/es 
1  6  rave/ 

32  » 

/ 

2700 

99              99 

3.3 
& 

BroKen 

1  9  to  22  mo 

64 

3334 

'  Rafter 

119 


TJrsrs  OM  CONCRETE  CUBES 

Continued 

IL./YIORTAR-I  PORTLAND  CEMENT:  2  SAND 

•5 

\ 

& 

ft/net 

Age 

\ 

Average 

I 

of 

of 

VO 

Compr 

Authority 

^^ 
^>» 

Stone 

Cube 

1 

Strength 

2 

Trap 

3  mo. 

8 

1964 

u.  3.  /see 

2 

99 

4     99 

4 

2834 

99              99 

3 

99 

3      99 

10 

2O3O 

91              99 

3 

99 

4      99 

5 

2803 

99              99 

6ravel 

28  da. 

2/25 

DycKerhoff 

3 

Cinder 

39      99 

3 

/098 

U.  5.  1898 

3 

99 

102     99 

3 

/634 

99              99 

4 

Trap 

3  mo. 

IO 

1957 

99            99 

4 

99 

4      99 

16 

2244 

99             99 

4 

Gran/te 

28  da. 

£ 

/607 

»    /B99 

4 

Pebb/es 

3  mo. 

5 

3206 

v    1836 

4 

Conglomerate 

7  foioda. 

25 

1565 

99    J899 

4 

19 

1  mo. 

30 

2399 

99             99 

4 

99 

3     99 

30 

2896 

99            99 

4 

99 

6      99 

26 

3796 

99             99 

4 

Slag 

52  da. 

8 

3392 

"9         /9OO 

4 

99 

05     99 

8 

4/35 

99            99 

4 

Cinder 

33      99 

3 

904 

99     /S98 

4 

99   >*.*,; 

98    99 

3 

1325 

99            99 

4 

BricK 

28      99 

6 

720 

99         /899 

4 

99 

3  mo. 

5 

275.7 

99             99 

4 

L/mestone 

6  eta. 

4 

1084 

99              99 

4 

99 

II  to  13  da 

8 

1676 

99            91 

4 

99 

/9  99  2O  99 

6 

2O40 

99             99 

4 

99 

52  da. 

5 

3604 

99         I9OO 

A 

99 

85    99 

5 

4-256 

99             99 

5 

Trap 

3  mo. 

/2 

2270 

9*        /899 

5 

99 

4      99 

6 

2321 

99              99 

Gravel 

28c/a. 

2367 

DycKerhoff 

5 

C/nder 

29  to  38  c& 

/5 

724 

U.  5.  1898 

120 


T£STS  OA/  COMCRETI  CUBES 

Continued 

JZ".  MORTAR  -  1  PORTLAND  CEMENT  :  2  SAND 

i 

I 

^ 

Kind 

Age 

1 

Average 

S: 

of 

of 

1 

Compr 

Authority 

^ 

Stone 

Cube 

v£> 

5ltengfh 

JS 

1 

5 

Cinder 

eotolOlda 

15 

IO&I 

U.  S.  I89Q 

^ 

O  ravel 

1  toZ^mo. 

7 

/477 

BaKer 

si 

99 

£    99    &     99 

2 

1742 

99 

is 

99 

12    "-A5     99 

2 

4583 

99 

vh 

99 

?O  *93O    99 

6 

227Q 

99 

| 

99 

3?  9936  " 

3 

2365 

99 

^S 

99 

35     9936     99 

2. 

3497 

99 

6 

Trap 

3  mo. 

/3 

1869 

U.  5.  1899 

6 

99 

4-  " 

7 

241  1 

99                *9 

6 

Gravel 

10  da. 

694 

A.W.Dow 

7 

Trap 

3  mo. 

15 

1466 

U.S.  /899 

7 

$6ravel,4Sfon& 

6       99 

2OOO 

EtoKer 

7 

99                99 

32  to  37  mo. 

6 

4428 

99 

8 

Trap 

3  mo. 

18 

1163 

U.S.   1899 

e 

99 

3       99 

to 

8/6 

99                 91 

5.18 
8.93 

Limestone 

19  to  22  mo. 

128 

2678 

ftaffer 

Iff.  MORTAR  -  IPopn  A  ND  CEMENT  :  3  5  A  ND 

5 

Gravel 

28  da 

/682 

DycKerhoff 
machine  mixed 

5 

Limestone 

3  mo.  2  da. 

& 

4043 

U.S.  /900 
hand  m/xed 

5 

99 

+  9                •)•> 

4 

3/87 

U.  S.   /900 

6 

Trap 

dofa. 

2 

858 

»      1898 

6 

19 

ntozoda 

3 

1  507 

99                   99 

6 

99 

4Zda. 

3 

2/92 

99                   99 

6 

99 

4-  mo\ 

15 

164-8 

99                   99 

6 

Gravel 

45  Gfa. 

/628 

A.W.Dow 

6 

99 

3  mo. 

2671 

99 

121 


TESTS  ON  COMCRCTZ  CUBES 

Continued 

HI  MORTAR  -/PORTLAND  CEMENT:  3  SAND 

\ 

K/r>d 

Age 

\ 

Average 

\ 

of 

of 

v^ 

Compr. 

Auffyor/fy 

fc> 
| 

Qfone 

Cube 

^ 

^ 

Strength 

6 

Gravel 

6mo. 

1844 

A.W.Dow. 

6 

•>? 

/year 

2824 

9  + 

6i 

99 

Z&cto. 

1515 

Dyekerhoff 

6 

Conglomerate 

7  To  IO  eta. 

23 

1420 

U.  5.  t899 

6 

99 

/  mo. 

28 

2/74 

99                  «» 

6 

99 

3  » 

30 

2522 

99                  99 

6 

99 

6  » 

23 

3//0 

99                99 

6 

Cinder 

Z9da 

3 

529 

»     I89B 

6 

99 

91  99 

3 

788 

99                M 

6 

BncK 

3  mo. 

7 

22O7 

99     1899 

6 

?Gr0Y.4BroK.sto. 

/  year 

283.5 

A.  W.  DOW. 

6 

3    99       3       99       99 

10  da. 

949 

99 

6 

3    99       3      99       99 

45     99 

1854 

99 

6 

3  »    3    "    » 

6  mo. 

2070 

99 

6 

3    1»      3       99       99 

/  year 

2751 

99 

6 

Limestone 

/O 

3067 

Barter 

6 

99 

7da. 

/584 

/?5%  voids  fi//ed 

6 

99 

fO  " 

1 

908 

/I.  W.Dow. 

6 

99 

30    99 

1795 

iZ5%vo/d$  f///ed 

6 

99 

45    99 

/ 

1791 

A.  W.  Dow. 

6 

99 

90  " 

2579 

I25%voids  f///ed 

6 

99 

3  mo. 

t 

2256 

A.  W.  Dow. 

6 

99 

6  » 

/ 

251  1 

99 

6 

99 

/year 

3 

2442 

99 

li 

99 

7&a. 

1 

/2B2 

Voids  filled 

7? 

99 

30  *> 

/ 

1672 

99                   99 

Ik 

99 

9099 

1 

1/28 

99                  99 

7.5 

I&9 

91 

19  to  22  mo. 

I2B 

1872 

6.  W.  Rafter 

10 

99 

lofa. 

1 

892 

75%voids  filled 

Tesrs  o/v  COA/CRETZ  CUBES 

______„,„    Continued 

HE  MORTAR-  /PORTLAND  CEMENT  :  3  SAND 

1 

VVv 

tf/nd 

4ge 

\ 

Average 

1 

of 

o-T 

I 

Gompr 

Attfhorifv 

1 

Stone 

Cube 

\ 
^ 

Strength 

10 

Limestone 

3otfa. 

/ 

472 

75%  voids  f/'J/ed 

IO 

99 

90  » 

/ 

919 

91              99             I") 

IF  MORTAR-  /PORTLAND  CEMENT  :  4  SAND 

a 

Trap 

4-  mo. 

/O 

/080 

U  B.  /893 

5 

O  rav  el 

2  Beta 

1273 

Dyctfer/ioff 

8i 

99 

28  ->-> 

1204 

*><> 

10 
& 

Limestone 

I9fo22mo. 

IO 

1735 

G.W  Rafter 

~Y.  MORTAR  -/PORTLAND  CEMENT  :  5  SAND 

10 

Trap 

4-  mo. 

12 

708 

U.  5.  1898 

"i5 

Limestone 

1  9  to  22  mo. 

32 

1554 

6.  W.  Rafter 

lb.4l 

W.  'MORTAR-  /PORTLAND  CEMENT  :  6  SAND 

12 

Trap 

4  mo. 

14 

625 

U.  5.   1898 

12 

Conglomerate 

7  to  /o  da 

25 

602 

•*      1699 

12 

a 

I  rno. 

30 

993 

11                99 

12 

99 

3   » 

30 

1076 

99                 99 

12 

99 

6    " 

21 

1408 

99                99 

16.66 

Lim&stone 

19  to  22  mo. 

4 

1427 

&Wffaffer 

When  exposed  to  ordinary  conditions  of  weather,  i  :2 14 
concrete  will  attain  in  two  or  three  months  a  unit  strength 
of  2,000  to  2,500  Ibs.  per  sq.  in.  Carefully  treated  specimens 
placed  in  water,  or  kept  under  cover  and  damp,  attain 
strength  of  2,500  to  3,500  Ibs.  per  sq.  in.  or  even  4,000  Ibs. 
It  is  not  possible  to  realize  this  latter  in  ordinary  work. 
The  former  represents  more  nearly  average  conditions  in  a 
structure. 

The  table  of  tests  on  concrete  cubes  in  the  five  pages 
given  herewith  are  taken  from  Municipal  Engineering, 
January,  1903.  The  specimens  were  nearly  all  12  in.  cubes. 

The  strength  of  concrete  in  cubes  has  only  limited  ap- 
plication in  the  proportioning  of  the  parts  of  a  structure. 
In  plain  concrete  columns  of  even  a  few  diameters  in 
length,  and  in  columns  having  small  longitudinal  steel  rods, 
a  safe  unit,  if  based  on  the  strength  of  a  cube  in  compres- 
sion, should  have  a  large  factor  of  safety  to  cover  the  un- 
certainties. A  factor  of  safety  of  eight  or  ten  for  concrete 
in  such  condition  would  be  about  equivalent  to  a  factor  of 
safety  of  four  for  concrete  confined  as  in  a  reinforced  con- 
crete beam  or  slab,  using  in  each  case  the  unit  determined 
by  the  cube  as  a  basis.  Carefully  prepared  specimens  load- 
ed exactly  centrally,  as  near  as  it  is  possible  to  effect  this 
condition,  are  not  safe  guides  to  the  design  of  members 
made  by  unskilled  labor,  whether  or  not  that  labor  has 
competent  supervision,  when  the  facts  are  such  that  a  lit- 
tle variation  from  perfect  conditions  makes  a  great  varia- 
tion in  the  unit  stress.  In  beams  and  slabs  the  concrete 
under  stress  is  confined  and  braced  in  such  a  way  that  a 
bad  batch  of  concrete  or  poor  work  has  not  a  very  detri- 
mental effect  on  the  compressive  strength.  Many  design- 
ers fail  utterly  to  appreciate  the  fact  that  in  columns  of 
plain  concrete,  or  concrete  and  longitudinal  rods,  the  con- 
crete is  under  entirely  different  conditions  than  in  a  beam 
or  slab,  and  that  these  unfavorable  conditions  in  the  con- 
crete column  are  in  parts  of  the  structure  whose  failure 
means  a  menace  to  the  entire  structure. 

The  tensile  strength  of  concrete  is  from  one- tenth  to 
124 


one-fifth  as  much  as  the  compressive  strength.  It  is  a 
more  uncertain  property  than  the  compressive  strength. 
In  general  the  tensile  strength  of  concrete  does  not  enter 
in  the  computation  of  the  structural  strength  of  reinforced 
concrete.  It  is  not  thereby  eliminated  from  the  problem. 
It  has  an  effect  on  the  location  of  the  neutral  axis,  a  fact 
very  generally  ignored  by  manufacturers  of  fine  formu- 
las. It  has  further  an  important  bearing  on  the  calculated 
deflection  of  a  beam.  The  tensile  strength  of  good  concrete 
suitable  for  reinforced  concrete,  well  aged,  is  from  200  to 
500  Ibs.  per  sq.  in.  If  a  reinforced  concrete  beam  be  de- 
signed for  500  Ibs.  per  sq.  in.  extreme  fibre  stress  in  com- 
pression, and  the  concrete  would  stand  500  Ibs.  per  sq. 
in.  in  tension,  the  beam  could  be  conceived  to  act  for  safe 
loads  entirely  as  a  concrete  beam.  Assuming  a  modulus 
of  elasticity  of  an  average  value,  equal  for  both  tension 
and  compression,  the  deflection  could  be  computed  as  for 
a  timber  beam.  For  example  if  the  modulus  of  elasticity 
is  3,000,000,  the  deflection  at  500  Ibs.  per  sq.  in.  would  be 
(by  the  ordinary  deflection  formula),  for  uniform  load, 
the  square  of  the  span  in  inches  divided  by  28,800  times 
the  depth  of  slab  or  beam  out  to  out,  in  inches.  If  then 
the  depth  of  slab  or  beam,  out  to  out,  is  one-twentieth  of 
the  span,  the  maximum  deflection  would  be  the  length  of 
the  span  divided  by  1440.  If  the  depth  is  one-tenth  of  the 
span,  the  maximum  deflection  would  be  the  length  of  span 
divided  by  2880. 

The  foregoing  rule  will  give  the  deflections  that  may 
be  looked  for  in  reinforced  concrete  floors  that  are  carry- 
ing their  loads  safely  without  cracks  on  the  tension  side  of 
beam  or  slab.  This  is  seen  to  be  small.  It  will  be  inverse- 
ly as  the  modulus  of  elasticity.  Thus  for  a  modulus  of 
6,000,000,  it  would  be  half  as  much  as  for  3,000,000,  and 
for  1,500,000,  twice  as  much.  If  cracks  occur' in  the  con- 
crete, the  deflection  will  be  greater.  Also  if  cracks  occur, 
the  steel  will,  at  the  crack,  carry  all  of  the  tensile  stress. 
This  is  doubtless  what  takes  place  in  many  beams,  namely, 
the  concrete  carries  all  or  nearly  all  of  the  tensile  stress 
125 


up  to  the  point  of  its  ultimate  strength ;  but  there  is  the 
possibility,  always  present,  of  the  concrete  cracking  and 
throwing  the  entire  tension  on  the  steel.  This  assumption 
of  the  action  of  the  stresses  in  a  reinforced  concrete  beam 
does  not  carry  with  it  warrant  for  using  any  less  steel 
than  would  be  used  if  the  concrete  were  totally  without 
tensile  strength,  neither  from  the  standpoint  of  the  unit 
stress  that  the  steel  may  take  nor  from  that  of  the  allowed 
stretch.  One  crack  in  a  beam  will  throw  all  of  the  stress 
on  the  steel,  and,  if  the  elongation  of  the  steel  is  excessive, 
other  cracks  would  be  a  natural  consequence. 

In  the  matter  of  the  shearing  strength  of  concrete  ex- 
perimenters have  reported  widely  different  results,  varying 
all  the  way  from  equality  with  the  tensile  strength  to  equal- 
ity with  the  compressive  strength.  This  wide  variation 
in  the  unit  shear  found  by  different  observers  is  just  what 
might  be  expected  in  a  material  such  as  concrete,  but  the 
failure  to  grasp  its  meaning  on  the  part  of  engineers  gen- 
erally is  not  so  easily  understood.  Elsewhere  in  this  book 
(Shear  on  Concrete  and  Its  Bearing  on  the  Design  of 
Beams)  the  author  has  pointed  out  that,  according  to  Mer- 
riman's  well-known  formula  for  combined  shear  and  ten- 
sion, if  the  tension  on  a  section  in  shear  be  zero,  the  ten- 
sile unit  stress  due  to  shear  alone  is  equal  to  the  shearing 
unit  stress.  It  is  the  simplest  kind  of  reasoning  to  deduce 
the  proposition  that,  unless  a  section  in  shear  is  in  com- 
pression at  the  same  time  to  overcome  the  tension  resulting 
from  the  shear,  the  shearing  strength  of  the  section  cannot 
exceed  the  tensile  strength  of  the  concrete. 

The  modulus  of  transverse  strength  of  concrete,  or  the 
calculated  extreme  fibre  stress  of  a  plain  concrete  beam  in 
bending  at  rupture,  cannot  be  much  more  than  the  tensile 
strength  per  sq.  in.  Experimenters  have  found  it  to  be 
between  one  and  one  and  one-half  times  the  unite  tensile 
strength.  A  safe  value,  where  stone  concrete  is  to  be  in 
bending  is  about  50  Ibs.  per  sq.  in. 

The  modulus  of  elasticity  of  concrete  is  the  subject  of 
this  paragraph.  Modulus  of  elasticity  is  sometimes  defined 
126 


as  the  ratio  of  stress  to  strain,  with  stress  further  defined 
as  an  axial  load  and  strain  the  deformation  (stretch  or 
shortening.)  The  stress  would  be  in  pounds  per  sq.  in. 
and  the  "strain"  in  linear  dimensions.  It  is  elementary 
arithmetic  that  there  can  exist  no  such  thing  as  a  ratio  be- 
tween pounds  and  inches,  or  between  any  measure  of 
weight  and  another  of  length.  Even  if  a  liberal  meaning 
is  applied  to  the  ratio,  it  necessitates  an  explanation  as  to 
the  terms  in  which  the  "strain"  must  be  given.  This 
forced  meaning  of  the  word  strain  is  totally  unnecessary 
and  does  not  possess  the  redeeming  feature  of  being  con- 
venient. The  language  is  rich  enough  in  terms  to  express 
the  particular  so-called  strain  referred  to  to  dispense  with 
a  blanket  term  that  must  be  further  defined  to  make  its 
meaning  clear  in  any  particular  case.  Deflection,  for  beams, 
stretch  or  elongation,  for  tension  members,  and  shortening, 
for  compression  members,  are  sufficiently  succinct  to  need 
no  explanatory  notes.  The  modulus  of  elasticity  is  de- 
fined under  the  heading  of  Steel  for  Reinforced  Concrete, 
and  its  definition  will  not  be  repeated  here.  The  modu- 
lus of  elasticity  of  concrete  varies  from  one  million  or  less 
to  five  or  six  million.  It  varies  with  the  intensity  of  stress ; 
it  varies  with  the  kind  of  aggregate  used ;  it  varies  with  the 
amount  of  water  used  in  mixing;  it  varies  with  the  atmos- 
pheric condition  during  setting.  An  average  value  may 
be  loo  per  cent,  too  great  or  50  per  cent,  too  small.  Added 
to  the  absolute  uncertainty  of  its  value  as  determined  in 
plain  concrete  tests  shrinkage  of  the  concrete  vitiates  as- 
sumptions as  to  relative  extensions  of  concrete  and  steel 
jointly  stressed.  The  workability  of  formulas  is  immense- 
ly hampered  by  introduction  of  the  modulus  of  elasticity. 
If  this  brought  in  any  needed  factor  or  tended  to  accuracy, 
it  might  be  justifiable.  It  does  neither.  It  is  merely  a  use- 
less refinement  of  absolutely  no  value  from  any  standpoint 
whatever. 

The  adhesion  of  concrete  to  steel  is  generally  stated  as 
one  of  the  useful  properties  in  the  combination  of  con- 
crete and  steel.    Concrete  plastered  on  flat  surfaces  of  steel 
127 


will  adhere  only  indifferently.  When  a  steel  rod  is  embed- 
ded in  concrete,  and  the  concrete  is  allowed  to  set  in  the 
air,  the  shrinkage  which  results  causes  the  concrete  to 
grip  the  steel  rod,  and  the  combination  of  adhesion  and 
friction  due  to  the  gripping  makes  the  rod  hold  in.  the  con- 
crete. The  force  necessary  to  pull  a  rod  out  of  concrete 
of  i  :2 14  mixture,  properly  made,  will  be  found  to  average 
about  500  Ibs.  per  sq.  in.  of  the  surface  of  the  rod  em- 
bedded, This  is  the  unit  found  on  ordinary  commercial 
steel.  On  such  surfaces  as  that  of  cold  rolled  steel  the 
adhesion  is  not  so  great,  but  cold  rolled  steel  has  no  place 
in  reinforced  concrete  construction.  The  surface  of  hot 
rolled  steel  is  sufficiently  rough  to  give  the  above  value  in 
adhesion.  In  the  case  of  a  unit  such  as  this  a  liberal  fac- 
tor of  safety  should  be  employed,  because  of  the  fact  that 
imperfect  concrete  or  poor  work  will  greatly  diminish  the 
available  strength.  A  safe  unit  for  this  adhesion  is  50 
Ibs.  per  sq.  in.  Round  or  square  rods  embedded  50  diame- 
ters in  concrete  at  this  unit  would  require  a  force  of  10,000 
Ibs.  per  sq.  in.  to  strain  the  adhesion  to  50  Ibs.  per  sq.  in. 
Fifty  diameters  is  therefore  a  proper  depth  to  anchor  a 
plain  round  or  square  rod  beyond  the  point  where  its  full 
stress  occurs. 

The  coefficient  of  expansion  of  concrete,  for  temperature 
variations,  does  not  differ  much  from  that  of  steel.  Its 
value  ranges  between  .0000055  and  .0000065  per  degree  R, 
while  that  of  steel  is  about  constant  at  the  higher  value. 
The  approximate  agreement  between  the  coefficient  in  steel 
and  concrete  is  of  great  value  in  reinforced  concrete  con- 
struction. If  there  were  a  large  difference,  change  in 
temperature  would  disrupt  a  concrete  member  of  a  struc- 
ture in  which  steel  were  embedded. 

Concrete  has  the  useful  property  of  being  probably  the 
best  preservative  of  steel  known.  Even  steel  that  is  some- 
what rusted  will,  after  being  buried  in  concrete  for  some 
time,  often  be  found  to  be  freed  of  its  rust.  It  has  been 
thoroughly  established  that  steel  buried  in  good  wet  con- 
crete will  be  permanently  preserved.  To  insure  the  pre- 
128 


servation  of  the  steel  a  wet  concrete  is  needed  and  one 
that  has  a  liberal  proportion  of  cement.  Dry,  rammed  con- 
crete is  porous  and  not  a  suitable  constituent  of  reinforced 
concrete  construction.  It  cannot  be  expected  to  preserve 
embedded  steel. 

Another  valuable  quality  of  concrete  is  the  capacity  to 
resist  fire  and  not  only  to  retain  its  integrity  and  the  great- 
er part  of  its  strength  through  fire,  but  also  to  act  as 
protection  to  steel  work.  There  is  perhaps  no  better  fire 
protection  commercially  available  for  steel  or  cast  iron 
columns  than  a  few  inches  of  cinder  concrete,  preferably 
held  together  with  rods  or  a  mesh  of  steel  of  some  sort. 
Not  all  concretes  have  the  same  fireproof  qualities.  Cinder 
concrete  is  one  of  the  best,  if  the  cinders  be  completely 
burned,  for  the  reason  that  the  aggregate  itself  being  un- 
affected by  heat  and  the  sand  being  practically  so,  there 
remains  only  the  cement  that  can  be  attacked  by  the  fire. 
Also,  on  account  of  the  cinder  concrete  being  porous,  its 
conductivity  is  low.  The  concretes  that  are  best  for  fire 
resisting  are  those  in  which  the  aggregates  are  least  affect- 
ed by  heat.  Sand  and  gravel  are  among  the  best  of  the 
hard  stones.  Broken  brick  would  make  a  good  fireproof 
concrete.  Sandstone  and  trap  are  also  good.  Granite  is 
not  so  good,  though  with  the  granite  broken  in  small 
pieces,  granite  concrete  would  stand  fire  better  than  solid 
granite.  Limestone  and  marble  are  not  good  fire  resistants 
on  account  of  the  fact  that  the  heat  calcines  them,  turn- 
ing them  into  quicklime.  Under  the  heat  of  a  fire  solid 
stone  cracks  and  spalls  off  in  large  chunks.  Concrete,  and 
especially  reinforced  concrete,  acts  quite  differently.  The 
sharp  corners  will  spall  off  for  a  small  depth,  but  the 
broad  surfaces  will  be  affected  by  a  calcination  acting  from 
the  surface  in.  The  depth  to  which  this  calcination  acts 
will  depend  upon  the  time  the  fire  lasts.  It  is  a  slow  pro- 
cess and  is  rendered  more  so  by  the  lessened  conductivity 
of  the  calcined  stone.  A  long  continued  fire  may  only  affect 
the  concrete  an  inch  or  so.  The  driving  off  of  the  water 
chemically  combined  with  the  cement  absorbs  a  large 
129 


amount  of  the  heat  of  a  fire.  The  water  does  not  separate 
from  the  cement  until  a  temperature  of  about  500  to  700 
degrees  F.  is  reached,  and  it  requires  a  much  higher  tem- 
perature than  this  to  complete  the  dehydration.  Concrete 
conducts  heat  so  slowly  that  a  column  of  ordinary  size 
would  have  to  be  in  a  hot  fire  for  many  hours  in  order 
to  have  the  high  temperature  of  the  fire  penetrate  to  its 
center. 

Concrete  may  be  used  for  flue  linings  where  the  tempera- 
ture does  not  exceed  about  600  deg.  F.  Neat  cement  tests 
made  at  the  Watertown  Arsenal  in  1902  did  not  show  any 
decrease  in  strength  up  to  a  temperature  of  600  deg.  F. 
Small  specimens  of  concrete  heated  in  an  oven  until  the 
heat  penetrates  the  interior  begin  to  lose  strength  at  about 
600  deg.  F.  for  trap  concrete  and  at  about  500  deg.  F.  or 
less  for  limestone  concrete. 

In  Engineering  World,  Jan.  4,  1907,  some  tests  are  re- 
corded that  purport  to  show  the  benefit  of  tile  as  a  fire 
protection  and  the  fallacy  of  depending  on  concrete  for  the 
purpose.  As  these  tests  have  been  given  wide  publicity,  it 
is  pertinent  to  examine  them  and  weigh  their  value.  Leav- 
ing out  unimportant  details  and  giving  results  in  close  ap- 
proximations, the  tests  were  as  follows.  A  column  about 
10  in.  square,  of  limestone  concrete,  at  the  age  of  23  months 
stood  a  crushing  load  of  about  3500  Ibs.  per  sq.  in.  Another 
column,  identically  made,  and  surrounded  with  3  in.  of  solid 
porous  tile,  laid  in  cement,  with  metal  fabric  in  the  hori- 
zontal joints,  was  subjected,  at  the  same  age  to  a  heat  of 
1500  deg.  F.  for  three  hours.  Without  applying  any  water 
to  cool  the  column,  presumably,  as  no  mention  is  made  of 
applying  water,  it  was  tested  the  next  day  and  stood  sub- 
stantially the  load  carried  by  the  column  that  was  not  sub- 
jected to  the  fire. 

Another  column,  identically  made,  wras  subjected  to  the 
same  heat  test  as  the  second,  without  protection,  and  at 
the  same  age.  After  the  fire  test  water  was  applied.  This 
column  failed  under  about  700  Ibs.  per  sq.  in. 


130 


The  points  about  these  tests  that  deserve  mention  are 
these: 

(a)  The   columns   were   of   limestone   concrete,   a   ma- 
terial acknowledged  to  be  poor  as  a  fire  resistant. 

(b)  The  tile  used  for  protection  was  solid    and  not,  as 
very  generally  used,  hol)o\V. 

(c)  The   tile   was   reinforced   in   the   joints   with   steel 
mesh,  a  very  unusual  and  expensive  construction. 

(d)  The  tile  covered  column  was  not,  apparently  del- 
uged with  water  to  test  its  integrity,  while  the  concrete  col- 
umn was  so  treated. 

(e)  One  hundred  by  700  equals  20  by  3500;  hence,  if  we 
consider  that  a  shell  of  concrete  was  totally  destroyed  by 
calcination    in    protecting   the    inner    core,    an    area   of   20 
square  inches  remained  good  for  the  full  unit  load.     This 
means  that  a  thickness  of  2%  in.  of  concrete  was  needed 
to  protect  the  inner  core,  as  against  3  in.  of  tile.     To  in- 
crease the  dimensions  of  the  concrete  column  by  3  in.  each 
way  would  be  very  much  cheaper  than  to  add  3  in.  of  tile 
of  any  sort,  and  the  result  is  a  column  that  is  vastly  more 
rigid  than  would  be  the  tile-covered  column. 

(f)  If  we  make  allowance   for  the  slenderness  of  the 
core  remaining  sound  in  the  bare  column  subjected  to  fire, 
the  comparison  in    (e)    would  be  still  more  favorable  to 
the    concrete    as    a    protection ;    since   the    slender   column 
would  not  be  expected  to  stand  as  high  a  unit  stress  as 
the  original  column. 

If  one  of  these  columns  had  been  made  16  in.  square,  and 
had  been  tested  on  the  same  basis  as  the  tile-protected  one, 
it  would  no  doubt  have  shown  that  much  less  than  a  3 
in.  thickness,  even  of  limestone  concrete,  would  serve  to 
preserve  the  core.  This  is  on  account  of  the  fact  that  the 
larger  core  would  retain  for  a  longer  time  a  low  tempera- 
ture, not  destructive  to  the  concrete,  and  would  take  up 
more  of  the  heat  that  would  otherwise  be  conducted  to  the 
interior. 

Concrete  is  superior  to  tile  as  a  fire  protection.  Tile,  on 
account  of  excessive  expansion  under  high  heat,  will  break 
131 


up,  when  in  long  elements,  as  surrounding  columns  or  in 
floor  arches  or  in  partitions.  This  was  strikingly  exhibit- 
ed in  the  Baltimore  and  San  Francisco  fires.  In  hollow 
blocks  of  tile  or  concrete,  on  account  of  the  fact  that  the 
thin  shell  becomes  heated  in  a  short  time,  the  expansion 
will  tend  to  crack  this  outer  shell  off.  It  is  a  nice  theory 
that  an  air  space  will  act  as  an  insulator  to  keep  excessive 
heat  from  the  vital  structural  parts,  and  it  would  hold  true 
for  moderate  heat.  A  hot  lire,  however,  or  fire  and  the  sub- 
sequent application  of  water,  demands  something  better 
than  would  be  required  for  insulation  against  moderate 
heat.  In  the  Baltimore  and  San  Francisco  fires  tile  arches 
suffered  very  greatly  from  the  breaking  off  of  the  soffit  or 
the  under  part  of  the  arch.  Reinforced  concrete,  if  it  be 
rationally  proportioned,  that  is,  with  the  beams  as  rectan- 
gular beams  and  not  T  beams,  as  advocated  in  this  book, 
will  have  ample  protection  of  the  steel  by  the  concrete  in 
the  lower  part  of  the  rectangle,  where  the  heat  of  the  fire 
is  most  destructive.  The  amount  of  the  protection  will  be 
in  agreement  with  the  size,  and  hence  with  the  importance 
in  the  structure,  of  the  steel  protected. 

It  is  more  economical  to  add  an  inch  or  two  of  concrete 
in  the  beam  or  column  than  to  fasten  tile  to  concrete.  In 
any  event  the  latter  is  easily  broken  off  by  expansion,  ex- 
posing the  thinly  covered  steel.  It  is  immeasurably  better 
to  add  concrete,  even  if  it  were  not  absolutely  needed  from 
the  standpoint  of  strength,  for  the  fire  protection  it  affords, 
than  to  load  a  structure  with  material  that  has  no  other 
use  than  fire  protection.  Such  foreign  material  is  an  extra 
load  on  the  structure  with  no  compensation  in  the  way  of 
added  strength,  whereas  a  little  extra  thickness  m  the  con- 
crete adds  greatly  to  the  strength  and  rigidity  and  longevity 
of  the  structure. 

It  is  true  of  reinforced  concrete  beams  in  a  greater 
measure  than  of  columns  that  concrete  added  for  fire  pro- 
tection is  cheaper  and  better  than  tile,  because  the  rigidity 
of  the  beams  is  increased  in  a  greater  proportion  by  a  small 
increase  in  thickness  than  would  be  a  column.  Also  it  is 
132 


more  difficult  to  make  tile  hold  on  the  under  side  of  a  beam 
than  to  make  it  stand  up  against  a  column.  Hanging  tile 
ceilings  have  proven,  in  recent  fires  to  be  specially  subject 
to  the  destructive  action  of  the  heat. 

Columns  need  protection  in  greater  amount  near  the  ceil- 
ing of  a  room  where  the  temperature  is  the  highest.  The 
practice  of  making  knee  braces  or  brackets  to  the  girders, 
as  often  followed,  is  an  excellent  one ;  as  these  serve  the 
double  purpose  of  laterally  bracing  a  building  and  of  add- 
ing concrete  about  the  head  of  a  column,  where  it  is  most 
needed  for  protection.  Ornamental  caps,  molded  in  the 
concrete,  also  serve  this  purpose. 

Reinforced  concrete  partitions  are  ideal  as  barriers 
against  the  progress  of  fire.  They  will  confine  a  fire  in  a 
room  as  the  sides  of  a  stove  confine  the  fire  within,  pro- 
vided, of  course,  that  the  fire  does  not  go  through  door 
openings. 

There  are  systems  of  floor  construction  that  make  use 
of  hollow  tile  in  a  rational  way.  In  one  of  these  rows  of 
tile  are  laid  on  flat  forms  at  the  ceiling  level,  and  between 
the  rows  ribs  or  beams  are  formed  in  reinforced  concrete, 
the  tile  serving  to  fill  the  space  between  the  ribs  and  to 
present  a  flat  surface  for  the  ceiling  plastering.  In  such 
construction  the  destruction  of  the  tile  would  be  of  little 
consequence. 

Another  system  makes  use  of  tile  to  fill  in  part  or  all 
of  the  space  between  a  bottom  layer  of  rich  concrete  an 
inch  or  two  thick,  reinforced  with  wire  mesh  and  steel 
rods,  and  a  top  layer,  two  or  three  inches  thick  of  plain 
concrete.  Sometimes  the  tiles  are  separated  and  concrete 
poured  between  them  to  form  ribs,  and  other  times  the 
tiles  are  laid  close.  The  tiles  in  this  construction  carry  the 
horizontal  shear,  and  the  concrete  above  them  takes  the 
compression.  Being  completely  enclosed  the  hollow  tiles 
are  protected  from  fire  by  the  concrete  with  its  embedded 
wire  mesh  and  rods. 

A  variation  in  the  above  described  floor  construction 
omits  the  top  layer  of  concrete.  Such  a  "floor"  might  be 

133 


suitable  for  a  sloping  roof,  where  the  live  load  is  not  ex- 
pected to  be  realized.  It  is  lacking  in  a  prime  essential 
of  substantial  construction  in  that  the  top  flange  consists 
solely  of  a  thin  sheet  of  tile,  made  up  of  a  great  number  of 
pieces  indifferently  joined  together  by  a  little  mortar  used 
in  laying  the  tile.  It  would  require  an  inspector  watching 
the  laying  of  every  tile  to  insure  the  filling  of  the  joints 
with  mortar.  Flushing  would  not  fill  these  joints,  as  the 
liquid  mortar  would  be  wasted  by  running  into  the  hollows 
of  the  tile,  if  flushing  were  attempted.  The  difficulty  in 
securing  filled  joints  lies  in  the  fact  that  the  joints  that 
count  are  where  the  thin  edges  of  the  tile  meet.  These 
remarks  apply  also  to  ordinary  tile  arches,  though  not  with 
equal  force,  since  the  thrust  in  an  ordinary  tile  arch  does 
not  approach  in  intensity  the  compression  in  a  system  of 
hollow  tile,  say  5%"  deep  with  %"  "metal"  having  i"  of 
concrete  or  mortar  underneath,  with  its  embedded  steel, 
on  a  span  of  sixteen  feet.  These  are  the  dimensions  of  a 
floor  measured  by  the  author. 

The  ability  of  concrete  to  resist  the  passage  of  water 
though  it  varies  all  the  way  from  that  of  a  sieve  to  that  of 
a  good  cork.  The  way  to  make  concrete  that  will  allow  the 
flow  of  water  through  it  with  little  impediment  is  to  mix 
it  dry,  that  is,  with  a  minimum  amount  of  water,  and  then 
to  ram  it  or  not  to  ram  it  in  place,  as  the  ramming  has  lit- 
tle to  do  with  it.  Ramming  will  bring  the  stones  together 
and  help  the  adhesion;  it  will  not  get  rid  of  the  general 
porosity.  The  only  way  to  make  concrete  of  itself  water- 
proof is  to  mix  it  very  wet.  Two  or  three  inches  of  wet 
concrete  will  hold  water  back  better  than  ten  or  twenty 
feet  of  dry  rammed  concrete.  This  would  appear  quite  ex- 
travagant, if  it  were  not  a  fact  proven  true  by  experience. 
The  fact  that  by  using  a  wet  mixture  in  the  thin  walls  of 
a  tank  water  can  be  completely  retained  is  sufficient  refu- 
tation of  the  charge  so  often  made  that  concrete  is  inher- 
ently porous. 

If  a  little  cement  mortar  be  mixed  in  a  tumbler,  the 
water  being  slowly  added,  it  will  be  seen  that  while  the 
134 


mixture  is  dry,  or  the  consistency  of  "moist  earth,"  there 
will  be  bubbles  in  it.  Ramming  or  compacting  the  mortar 
will  not  serve  to  eliminate  these  bubbles  but  may  break 
them  up.  The  air  is  imprisoned  and  has  not  the  buoyancy 
to  force  its  way  to  the  surface.  Some  of  it  may  be  forced 
out  on  account  of  the  porosity  of  the  mortar,  but  the  ulti- 
mate result  is  only  a  reduction  of  the  magnitude  of  the 
pores.  When  more  water  is  added,  the  mortar  assumes  a 
liquid  consistency,  and  the  air  bubbles  will  rise  to  the  sur- 
face. It  is  urged  against  liquid  concrete  that  the  excess 
of  water  above  that  which  the  cement  absorbs  in  the  hard- 
ening process,  when  it  evaporates,  will  leave  voids  in  the 
concrete.  By  this  reasoning  it  is  concluded  that  wet  con- 
crete will  be  porous,  and  by  reversing  it,  it  is  contended 
that  the  proper  consistency  for  the  maximum  watertight- 
ness  is  that  in  which  there  is  just  enough  water  for  the 
needs  of  the  cement  in  hardening.  Reasoning  like  this 
would  make  a  cork  a  very  poor  thing  to  keep  back  water. 
Cork  is  quite  porous.  It  can  be  made  to  absorb  hot  water, 
and  it  will  give  it  off  again  in  drying.  Its  substance  can 
be  compressed  to  a  fraction  of  its  normal  volume.  And 
yet  it  is  practically  perfectly  water  tight,  while  other  woods 
or  barks,  weighing  much  more  and  apparently  much  more 
dense,  do  not  possess  this  property.  The  best  way  to  keep 
water  out  of  concrete  is  to  put  lots  of  water  in  it  in  the 
manufacture.  A  rich  concrete  is  necessary,  for  water  tight- 
ness, and  a  mixture  that  will  compact  well.  Small  gravel 
is  good  for  this  purpose  because  of  the  density  of  the  stones 
themselves  and  because  gravel  has  the  property  of  packing 
well  on  account  of  the  comparatively  small  friction  between 
the  stones.  Thorough  mixing  is  another  necessity,  to  in- 
corporate the  cement  and  water  and  to  distribute  it  uni- 
formly throughout  the  mass. 

Some  clay  in  the  sand  in  a  finely  divided  state  or  added 
to  the  mixture,  if  it  can  be  thoroughly  mixed  through  flie 
mass,  or  clay  in  a  semi-liquid  state  has  been  known  for 
some  time  to  add  to  the  density  and  watertightness  of  con- 
crete. In  Eng.  News,  Sept.  26,  1907  Mr.  Richard  H.  Games 
135 


describes  some  tests  in  which  5  to  10%  of  the  cement  of 
mortar  was  replaced  with  an  equal  quantity  of  dried  and 
finely  ground  colloidal  clay  intimately  mixed  with  the  ce- 
ment. The  result  was  a  watertight  product  much  stronger 
than  the  cement  mortar. 

Some  concretes  become  more  impermeable  with  age. 
Concrete  which  when  new  may  not  be  quite  watertight, 
may  become  so  by  the  action  of  water  passing  through  it. 
This  may  be  due  partially  to  uncombined  silicates  being 
dissolved  by  the  water  and  re-deposited,  or  to  the  swell- 
ing of  the  tine  cement  particles  in  the  presence  of  water. 
Possibly  also  solid  matter  in  suspense  in  the  water  clogs 
up  the  interstices  as  a  filter  becomes  clogged. 

It  is  true  that  even  with  wet  concrete  pockets  are  lia- 
ble to  form,  and  poor  batches  may  find  their  way  into  a 
wall  or  tank.  These  can  be  stopped  up  or  remedied  by 
rich  mortar  filling  all  of  the  pores.  In  a  cistern  built  under 
the  author's  supervision  perfect  watertightness  was  attained 
by  the  use  of  wet  concrete  and  careful  plastering  of  all 
holes  with  neat  mortar  while  applying  a  wash  of  neat  mor- 
tar with  a  brush,  after  thoroughly  wetting  the  surface. 
The  neat  cement  wash  exposed  at  once  any  large  pores  in 
the  concrete,  and  these  were  plastered  up  by  troweling. 
This  wash  was  made  the  consistency  of  thick  cream.  After 
24  hours  the  surface  was  again  washed  with  the  cement 
cream,  and  a  third  coat  was  applied  after  another  interval 
of  24  hours.  In  addition  to  this  treatment  the  contractor 
washed  the  surface  with  a  mixture  of  hydrated  lime  and 
soft  soap.  The  author  is  of  the  opinion  that  this  latter 
did  not  affect  the  watertightness,  as  it  appeared  not  to  be 
permanent.  (See  Eng.  News,  Sept.  28,  1905,  p.  330). 

That  concrete  of  itself  can  be  made  practically  water- 
tight is  proven  by  numerous  tanks  and  sewer  pipes  and 
some  water  pipes  that  have  been  made  of  concrete  un- 
treated and  not  "waterproofed."  Tests  of  mortar  and  con- 
crete have  demonstrated  their  ability  to  withstand  water 
under  pressure.  In  Trans.  Assoc.  of  C.  E.,  Cornell  Uni- 
versity, Vol.  XIII;  Mr,  A.  B.  Moncrieff  describes  tests  on 
136 


blocks  of  concrete,  2  ft.  each  way,  in  which  a  water  pipe 
was  embedded,  the  pipe  being  surrounded  by  a  5  in.  bulb  of 
hemp  and  small  rope.  Some  of  these  test  blocks  allowed 
only  1-50  of  a  pint  of  water  to  pass  through  in  two  weeks 
under  100  ft.  head  of  water.  At  the  end  of  80  weeks  the 
tests  were  repeated  with  a  head  of  200  ft.  The  results 
were  about  the  same. 

In  Engineering  News,  June  26,  1902,  p.  517,  Messrs,  J. 
B.  Mclntyre  and  A.  L.  True  describe  some  tests  on  gravel 
concrete  5  in.  thick  that  had  set  24  hrs.  in  air  under  a 
damp  cloth  and  a  month  in  water.  They  found  that  con- 
crete specimens  containing  i  :i  mortar,  and  in  which  the 
mortar  was  30  to  45%  of  the  whole  mass,  were  watertight. 
These  stood  pressures  as  high  as  80  Ibs.  per  sq.  in.  for  24 
hrs.  without  leak.  Some  of  the  concrete  specimens  having 
i  :2  mortar  and  40  to  45%  of  mortar  in  the  mixture  were 
also  impermeable,  as  well  as  the  1 :2 14  and  1 12.5  14  mixtures. 

In  Engineering  Record  Dec.  14,  1907,  p.  661,  some  tests 
are  given  by  R.  T.  Surtees,  C.  E.  Newton-le-Willows,  Lan- 
cashire, England,  that  show  remarkable  results.  Some 
plugs  of  concrete  5  in.  thick  were  made  in  pipes  and  water 
under  pressure  was  brought  to  bear  against  them.  Two 
of  these  stood  a  pressure  of  35  to  50  Ibs.  per  sq.  in.  for 
thirty  days  without  leakage.  In  a  repetition  of  the  tests  one 
specimen  was  allowed  to  set  where  exposed  to  the  sun  most 
of  the  day,  another  was  allowed  to  set  in  a  shaded  place, 
and  two  others  were  allowed  two  days  under  a  damp  cloth 
and  28  days  immersed  in  water.  The  concrete  of  the  first 
shrunk  and  did  not  fill  the  pipe.  The  second  showed  a  very 
slight  dampness,  which  soon  took  up.  The  other  two  were 
perfectly  watertight.  The  pressure  on  these  tests  was  in- 
creased to  260  Ibs.  per  sq.  in.  With  pressure  varying  be- 
tween 50  and  260  Ibs.  for  two  days  no  sign  of  dampness 
appeared  on  the  outside.  One  of  the  blocks  was  cut  out 
to  see  how  far  the  water  had  penetrated.  It  was  seen  to 
be  traceable  for  a  distance  of  only  iVs  in.  The  concrete  of 
these  tests  was  made  of  two  mixtures,  namely,  I  part  of 
cement,  i  part  of  sand,  i  part  of  crushed  gravel,  i  part  of 

137 


gravel  screened  to  %  in.,  and  a  mixture  of  1:1:1^:1%  of 
the  same  ingredients  respectively.  The  same  experimenter 
made  a  reinforced  concrete  pipe  and  subjected  it  to  120  Ibs. 
No  sign  of  dampness  appeared  on  the  outside  of  the  pipe. 

Troweling  increases  the  impermeability  of  concrete. 
Troweling  should  be  done  in  such  positions  as  the  top  sur- 
face of  an  arch  and  the  exposed  surface  of  a  sea  wall. 

Concrete  has  been  found  to  be  suitable  for  tanks  in  which 
to  freeze  water  in  the  manufacture  of  ice.  At  the  annual 
meeting  of  the  Am,  Soc.  of  Refrigerating  Engineers,  at 
New  York,  in  1907,  Mr.  Abram  Day  describes  some  ice 
tanks  of  reinforced  concrete  that  have  been  used  for  some 
years  with  satisfaction.  In  some  tanks  Mr.  Day  used  1:1 13 
concrete  of  trap  rock  and  in  others  iVz  \iVz  :2Vz.  He  finds 
the  best  size  of  aggregate  to  be  s.tone  about  %  in.  to  ^  in. 
The  inside  of  his  tanks  are  either  left  rough  or  washed 
with  neat  cement.  No  waterproofing  is  used.  [See  Eng. 
News,  Dec.  12,  1907,  and  Ice  and  Refrigeration,  Dec.  1907 .] 

Another  useful  property  of  concrete  was  brought  out 
at  the  meeting  referred  to  in  the  previous  paragraph.  Mr. 
John  E.  Starr  described  a  nine-story  cold-storage  ware- 
house built  entirely  of  reinforced  concrete,  with  a  double 
facing  wall  filled  in  between  with  cork.  Additional  insula- 
tion was  also  provided  by  coating  the  tops  of  all  floors 
with  cork  boards,  two  to  four  inches  thick.  It  is  a  remark- 
able fact  that  though  the  inside  of  this  house  is  frequent- 
ly at  as  low  a  temperature  as  five  below  zero,  R,  with  the 
outside  wall  above  100  deg.  F.,  no  signs  of  cracking,  due  to 
expansion,  have  ever  been  noticed. 

Hollow  blocks  of  concrete  afford  excellent  insulation 
against  moderate  heat  or  to  retain  heat  in  a  building. 

The  ability  of  concrete  to  stand  weather  and  atmospheric 
conditions  is  often  much  better  than  that  of  the  stone  com- 
posing the  aggregate  of  the  concrete.  A  poor  stone  is 
improved  by  being  made  into  concrete  and  surrounded  and 
protected  by  a  mortar  of  sand  and  cement.  Hard  stone 
such  as  granite  and  trap  are  not  as  durable  nor  as  strong, 
made  into  concrete,  as  the  original  stone.  These  stones 
138 


however,  make  the  strongest  kind  of  concrete,  and  the  use 
of  trap,  especially,  in  concrete  has  the  advantage  of  being 
a  means  of  utilizing  this  stone  for  building  purposes,  when 
it  would  be  scarcely  possible  to  use  it  at  all  as  a  building 
stone.  Trap  is  very  refractory  under  the  dressing  tool  and 
can  only  be  employed  in  rough  blocks.  Some  stones  that 
would  develop  planes  of  fracture  in  a  structure  made  of 
block  stones  have  these  planes  fractured  in  the  crusher. 
They  are  therefore  rendered  safe  against  failure  by  crack- 
ing. Stones  that  by  themselves  suffer  surface  disintegra- 
tion would  be  subject  to  the  same  action,  if  exposed  on 
the  surface,  though  the  cement  and  sand  of  the  concrete 
will  protect  them  very  materially.  If  the  mortar  of  the 
concrete  be  worked  to  the  surface,  stone  that  would  suffer 
surface  disintegration  may  be  quite  durable  in  concrete. 
Slag  cement  should  not  be  used  for  concrete  that  will  be 
dry,  if  used  at  all,  it  should  be  where  the  concrete  is  al- 
ways wet.  Good  Portland  cement  concrete  will  be  durable 
either  wet  or  dry. 

One  of  the  most  trying  situations  for  concrete  is  sea 
water  between  high  and  low  tides.  Much  has  been  writ- 
ten on  the  subject  of  the  chemical  effect  of  the  salts  of 
sea  water  on  cement  and  concrete.  That  the  deterioration 
is  a  surface  action  almost  entirely  and  that  it  is  generally 
confined  to  the  zone  between  high  and  low  tide  levels 
suggests  that  the  action  is  at  least  partially  mechanical. 
The  formation  of  salt  crystals  in  the  pores  of  the  concrete, 
by  the  evaporation  of  the  salt  water,  by  their  swelling  ac- 
tion may  have  something  to  do  with  this  surface  disin- 
tegration. 

It  is  a  fact,  and  one  that  the  author  has  found  to  be 
not  generally  known  by  practical  chemists,  that  silicates, 
when  ground  to  a  fine  powder,  glass,  for  example,  are  solu- 
ble in  acids  and  alkalies  that  do  not  affect  the  solid  lumps. 
Ground  glass  is  even  soluble  in  pure  water.  Crushed  rock 
will  make  soil  in  a  very  short  time,  whereas  the  same  rock, 
in  large  pieces,  may  withstand  the  weather  a  long  time 
before  disintegrating.  Water  acts  on  the  ground  rock  in 
139 


a  very  short  time.  It  is  said  that  holes  can  be  blasted  in  the 
rock  in  certain  parts  of  the  Florida  Keys  and  crops  planted 
in  the  broken  stone.  Cement  clinker  is  a  sort  of  glass. 
When  ground  to  a  fine  powder,  it  is  partially  soluble  in 
water.  This  can  be  seen  by  stirring  cement  in  a  large 
quantity  of  water,  preferably  hot.  A  glass  like  scum  forms 
on  top  of  the  water  after  it  stands  a  while.  If  allowed  to 
absorb  water  and  to  harden  without  being  subject  to  con- 
ditions that  take  away  the  water,  cement  will  unite  with 
the  water  and  form  a  permanent  compound.  If  the 
amount  of  water  is  stinted,  as  in  the  "moist  earth"  con- 
crete mixtures  so  popular  with  many,  it  is  impossible  for 
all  of  the  grains  of  cement  to  find  sufficient  water  to  make 
them  into  a  stable  compound.  They  remain,  therefore,  in 
some  degree,  in  the  state  of  ground  silicates,  easily  dis- 
solved by  water.  With  Portland  Cement,  sloppy  concrete 
and  a  smooth  finish  on  the  surface  exposed  to  sea  water, 
or  any  wave  action,  is  the  best  precaution  against  dissolv- 
ing action. 

The  continuous  washing  of  the  surface  of  concrete  by 
waves  of  water,  either  salt  or  fresh,  would  be  expected  to 
carry  away  any  uncotnbihed  silicates  in  the  cement ;  where- 
as, if  the  water  were  still,  the  dissolved  silicates  would  not 
be  carried  away,  but,  as  is  possibly  the  case  in  still  water, 
they  would  be  redeposited  in  the  pores  of  the  concrete. 
It  is  probably  this  dissolving  that  is  responsible  for  the 
pitting  and  roughening  of  cement  pavements  caused  by 
rain.  While  this  is  a  chemical  action,  the  mechanical  action 
of  the  beating  water  supplies  the  destructive  element.  Dry 
concrete  and  excessive  troweling  to  give  a  glossy  surface 
are  very  commonly  resorted  to  by  pavers.  It  is  not  un- 
common to  see  the  same  pavements  pitted  after  some  time 
of  exposure  to  weather. 

In  sewers  and  water  pipes  this  is  not  exhibited  in  the 
same  way,  because  mud  deposits  in  the  pores  and  protects 
the  concrete  where  the  scour  would  be  the  most. 

Concrete  subject  to  the  action  of  sea  waves  should  have 
a  coat  of  rich  mortar  plastered  very  smoothly.  Facing  con- 

140 


Crete  with  granite  between  high  and  low  tide  levels  is  very 
often  practiced.  This  is  a  sure  way  of  rendering  a  sea 
wall  permanent. 

There  is  a  cement  called  iron-ore  cement,  manufactured 
in  Germany,  which  is  said  to  resist  the  action  of  sea  water. 
This  cement  is  made  of  iron-ore  and  limestone  instead  of 
clay  and  limestone. 

The  weight  of  stone  concrete  generally  runs  about  150 
Ibs.  per  cu.  ft.  Heavy  stones,  such  as  granite  and  lime- 
stone may  exceed  this.  Sandstone  concrete  may  weigh 
less.  Concrete  mixed  with  a  minimum  amount  of  water 
will  weigh  less  than  medium  or  wet  concrete,  a  fact  which 
testifies'  to  the  porosity  of  the  former.  The  weight  of 
sandstone  is  about  150  Ibs.  per  cu.  ft.;  of  granite,  170;  of 
limestone,  170. 

Cinder  concrete  weighs  about  no  Ibs.  per  cu.  ft.  when 
dry.  Wet  cinder  concrete  should  be  calculated  to  weigh 
about  125  Ibs.  per  en.  ft.  in  designing  the  forms. 

Notes  on  General  Design  and 
Construction 

Under  this  heading  will  be  given  some  notes  bearing  on 
the  general  design  and  treatment  of  structures  that  do  not 
come  under  the  head  of  any  of  the  other  general  subjects 
treated. 

DRAINAGE.  Retaining  walls  and  arches  should  be  well 
drained  by  a  system  carefully  planned  to  perform  its  work. 
Iron  or  steel  pipes  should  be  avoided,  if  the  water  passing 
through  them  runs  over  the  exposed  face  of  the  wall ;  be- 
cause the  rust  will  disfigure  the  wall.  A  collapsible  wooden 
core,  say  of  a  round  or  square  piece  split  longitudinally 
on  a  slant,  would  allow  the  removal  of  the  pieces  separate- 
ly. Or  a  box  of  thin  wood  could  be  used  and  broken  up 
on  removal.  Or  a  smooth  hard  wood  core  could  be  used 
and  drawn  out  before  the  concrete  has  a  hard  set.  Clay 
tiles  placed  in  concrete  make  good  permanent  drains.  In 

141 


building  a  wall  there  should  be  a  lot  of  loose  stones 
placed  where  water  would  collect  and  where  the  drain  is 
located,  so  that  it  will  not  clog  up.  It  would  not  be  out 
of  place  to  have  a  drainage  system  in  a  building.  In  a  fire 
damage  by  water  is  often  greater  than  by  the  fire  itself. 
A  fire  in  the  upper  story  of  a  building  may  be  extin- 
guished by  the  application  of  water,  which,  if  it  is  not 
carried  away,  may  run  down  the  stairs  to  floors  below 
and  work  damage  there. 

PROVISION  FOR  EXPANSION  AND  CONTRACTION.  Calcula- 
tions for  temperature  stresses  in  concrete  are  of  little  if 
any  use.  Shrinkage  in  concrete  due  to  setting  in  the  air 
is  a  more  important  factor  in  changing  its  size  than  tem- 
perature variation.  If  this  were  elimnated,  calculations 
for  temperature  changes  would  have  some  meaning.  How- 
ever the  actual  change  in  temperature,  as  in  an  arch,  would 
not  be  very  much,  especially  if  the  arch  is  one  having  fill 
over  it.  Concrete  and  earth  are  both  poor  conductors  of 
heat,  and  the  range  of  temperature  in  the  body  of  the  arch 
would  not  approach  that  which  could  be  expected  to  take 
place  in  a  steel  structure.  It  is  usually  in  arches  that 
temperature  stresses  are  the  most  minutely  elaborated. 
There  is  undoubtedly  more  or  less  uncertainty  in  the 
stresses  in  an  arch  due  to  temperature  changes,  but  the 
same  is  true  in  a  larger  measure  of  the  effect  of  shrinkage. 
Uncertainties  should  be  covered  by  a  factor  of  safety  or 
by  liberal  design :  it  does  not  minimize  them  to  attempt 
to  cover  them  by  fictitious  though  elaborately  calculated 
stresses.  Steel  reinforcement  in  all  parts  of  an  arch  or 
other  structure  is  one  of  the  best  safeguards  against  shrink- 
age and  temperature  stresses.  To  build  a  structure  so  that 
shrinkage  may  take  place  during  the  building  is  another. 
In  an  arch  it  would  be  better,  where  possible  to  place  the 
entire  arch  ring,  leaving  a  groove  and  steps  for  the  span- 
drel wall  to  be  poured  after  the  forms  of  the  arch  ring  are 
removed.  In  a  building  walls  or  partitions  would  be  bet- 
ter to  be  separate  from  the  columns,  let  into  recesses  in 
the  latter  and  placed  after  the  columns  have  set.  In  a  long 

142 


structure  two  sets  of  columns  and  girders  at  a  dividing 
plane  would  give  opportunity  for  shrinkage  to  act.  Pro- 
vision for  shrinkage  is  only  a  makeshift,  and  a  useless 
one,  unless  carried  down  to  the  foundation. 

ARCHES  IN  SERIES.  In  a  long  line  of  arch  spans  it  is 
legitimate  to  make  the  piers  between  the  adjacent  spans 
heavy  enough  to  be  rigid  against  live  load  only  on  any 
span,  if  the  arches  are  equal  and  the  dead  load  thrust  bal- 
anced. However,  there  should  be  an  occasional  pier  that 
will  take  the  full  thrust  of  one  span,  so  that  if  one  span 
should  fail,  the  entire  system  will  not  come  down.  Every 
third  or  fifth  pier  may  be  an  abutment.  Forms  should  not 
be  removed  in  a  long  line  of  arches  in  a  span  adjacent  to 
a  pier  that  is  not  capable  of  acting  as  an  abutment. 

Box  CULVERTS.  Flat  slab  tops  on  box  culverts  are  pre- 
ferable to  arches  for  several  reasons.  They  do  not  re- 
quire abutments  but  only  supporting  side  walls.  When 
fill  is  being  made  between  wooden  trestle,  a  flat  top  box 
culvert  can  be  introduced  between  trestle  bents,  where 
often  an  arch  culvert  and  its  abutments  would  require 
the  removal  of  one  or  two  bents. 

TANKS.  There  is  not  much  economy,  if  any  in  using 
a  reinforced  concrete  tank  as  compared  with  a  steel  tank. 
The  shell  of  a  steel  tank  can  be  stressed  to  20,000  Ibs. 
per  sq.  in.  or  more,  and  the  tank  will  be  safe  and  tight. 
Many  oil  tanks  are  designed  with  a  unit  stress,  on  the 
vertical  section,  of  about  24,000  Ibs.  per  sq.  in.  Steel  em- 
bedded in  concrete  and  stressed  to  these  amounts  would 
crack  the  concrete,  and  of  course  the  cracks  would  destroy 
the  value  of  the  tank  as  a  receptacle  for  liquids.  There  is 
not  much  difference  in  cost  per  pound  of  steel  ro'ds  placed 
in  a  rinforced  concrete  tank  and  the  steel  shell  in  place 
and  riveted.  There  is-  therefore  a  large  margin  in  favor 
of  the  steel  tank.  There  may,  however,  be  cases  where  re- 
inforced concrete  tanks  would  be  more  suitable,  and  there 
may  be  cases  where  they  would  be  more  economical.  The 
greater  lasting  quality  of  reinforced  concrete  makes  it  more 
desirable  in  many  cases  than  steel.  Tanks  with  small  ten- 

143 


sion  in  the  shell  may  require  to  be  made  of  steel  plates 
much  thicker  than  the  mere  tension  would  demand,  so 
that  small  tanks  might  be  as  cheap  in  reinforced  concrete 
as  in  steel. 

CISTERNS.  A  cistern  with  an  approximately  flat  bot- 
tom would  often  be  better  to  have  the  bottom  somewhat 
concave.  Shrinkage  cracks  are  less  liable  to  occur  in  a 
curved  bottom,  and  with  the  bottom  concave  the  cistern 
can  be  emptied  and  cleaned  better  than  with  a  flat  bottom. 

SMALL  COLUMN  PEDESTALS.  In  making  small  column 
pedestals  it  is  well  to  make  as  few  different  sizes  in  a  given 
structure  as  practicable,  at  the  expense  of  using  more  con- 
crete than  is  required  in  some  of  them.  It  simplifies  the 
form  work  to  make  duplicate  sizes.  Steps  in  the  sides 
are  preferable  to  a  batter,  especially  if  the  top  is  small  and 
the  batter  large.  It  is  hard  to  pour  concrete  in  the  small 
hole  and  hard  to  tamp  it  through  the  same. 

STAIR  SUPPORTS.  Slabs  and  beams  for  the  support  of 
stairs  are  to  be  calculated  for  a  span  equal  to  the  hori- 
zontal projection  and  not  the  actual  length,  though  of 
course  the  weight  of  the  parts  are  found  from  their  actual 
dimensions.  When  triangular  blocks  are  cast  on  a  slab 
for  the  steps,  these  should  not  be  counted  in  any  part 
of  the  depth  of  slab.  The  slab  should  be  proportioned  for 
a  depth  exclusive  of  these  blocks.  At  angles,  as  where  a 
landing  joins  the  slope  of  the  stairs,  there  should  not  be 
a  sharp  corner  in  the  slab:  there  should  be  a  thickening 
of  the  slab,  and  reinforcing  rods  should  be  given  gentle 
curves,  say  with  a  radius  50  to  80  times  the  diameter  of 
rod. 

BEAMS  AND  GIRDERS.  As  few  sizes  as  possible  of  beams 
and  girders  should  be  used,  and  their  spacing  should  be 
as  regular  as  practicable.  For  economy,  the  deeper  the 
beam  the  less  it  will  weigh,  just  as  in  wooden  construction 
and,  generally,  in  steel  work.  However,  deep  beams  loaded 
to  their  capacity  are  apt  to  be  weak  in  shear.  Also  deep 
beams  may  be  too  narrow  for  other  reasons.  They  may, 
further,  encroach  on  clearance,  or  they  may  necessitate  ad- 

144 


ditional  height  to  a  building.  Girders  and  beams  should 
be  placed  at  columns  rather  than  near  the  columns  so  that 
they  will  help  to  stiffen  the  building. 

SHAFT  HANGERS.  Shaft  hangers  may  be  attached  to 
beams  by  means  of  bolts  placed  in  the  concrete  having 
the  threaded  end  projecting  to  receive  the  hanger;  or 
threaded  castings  may  be  built  in  the  beam,  either  in  the 
side  or  bottom,  to  these  the  hanger  may  be  attached,  or 
timbers  or  steel  angles  may  be  bolted  on;  or  pieces  of 
gaspipe  may  be  left  through  the  beams  near  the  bottom 
and  bolts  run  through  them  to  which  timbers,  or  blocks 
or  longitudinal  angles  may  be  bolted;  or  clamps  may  be 
used  on  the  beams,  held  on  by  friction. 

HOLES  FOR  PIPES  AND  WIRES.  Holes  should  be  left  in 
floors  in  the  building  of  them  for  all  pipes  and  wires  that 
may  be  placed.  It  would  be  better  to  leave  too  many  than 
not  to  leave  any  or  not  to  leave  enough.  It  is  easy  to  ce- 
ment up  such  holes  but  very  difficult  to  cut  them  in  hard- 
ened concrete. 

BATTERED  ABUTMENTS.  It  is  unnecessary  to  give  abut- 
ments a  batter  on  the  front  face.  It  appears  to  be  a  rudi- 
ment of  some  popular  notion  of  stability  that  a  small  bat- 
ter, say  of  i  to  12,  will  add  rigidity  to  abutments,  wing 
walls,  sides  of  culverts  (inside),  etc.  It  does  not  pay  for 
the  trouble. 

VERTICAL  PIPES.  If  possible  vertical  pipes  should  be  lo- 
cated where  they  will  not  run  between  a  column  and  its 
lire  protection.  Expansion  due  to  heat  will  cause  the  pipes 
to  buckle  and  will  tend  to  pry  off  the  lire  protection.  This 
will  apply  to  any  building  where  the  fire  protection  is 
separate  from  the  structural  column,  as  in  cast  iron  or 
steel  column  construction. 

HEAVY  GIRDERS.  In  general,  reinforced  concrete  is 
neither  appropriate  nor  economical  for  very  heavy  girders, 
either  long  span  girders  or  short  ones  taking  heavy  con- 
centrations. Steel  girders  are  more  suitable  in  such  cases, 
In  very  long  spans  the  dead  weight  of  the  girder  is  ex- 
cessive :  in  short  spans  carrying  heavy  concentrations  the 

145 


embedment  of  the  steel  is  apt  to  be  insufficient  for  the 
stress,  also  shearing  stresses  are  difficult  to  provide  for. 
Shallow  beams  are  best  made  in  steel  also,  as  concrete 
beams  shallow  in  depth  are  clumsy  on  account  of  having 
to  be  so  wide. 

SLENDER  COLUMNS.  Slender  columns  should  not  be  at- 
tempted in  concrete.  They  are  better  to  be  of  cast  iron  or 
of  steel,  protected  with  concrete  if  necessary. 

REINFORCING  WALLS  AT  CORNERS.  Walls  that  meet  at  an 
angle  should  be  tied  together  at  the  intersection  to  pre- 
vent cracking  at  the  corner. 

SCHEME  FOR  FLOOR  SUPPORT.  A  very  simple  and  efficient 
reinforced  concrete  floor  for  either  a  highway  or  a  rail- 
road bridge  can  be  made  by  running  rods  transversely  from 
girder  to  girder  to  act  as  bottom  reinforcing  rods  in  the 
floor  slab.  The  rods  should  be  plain,  round,  threaded  on 
the  ends,  and  should  pass  through  the  steel  work,  Holes 
being  left  for  the  purpose.  If  the  slab  rests  on  a  shelf  on 
the  side  of  a  beam  or  girder,  the  holes  may  be  in  the  web 
just  above  the  shelf.  If  it  is  a  through  span,  the  slab  rest- 
ing on  the  bottom  flange  of  the  girder,  some  of  the  rivet 
holes,  say  at  intervals  of  6  or  9  ins.,  may  be  left  open.  In 
a  deck  span  the  web  plate  may  be  extended  to  take  the 
holes  for  reinforcing  rods.  This  slab  construction  is  ad- 
mirable for  highway  bridges.  The  entire  roadway  may 
be  one  continuous  slab  from  truss  to  truss  or  girder  to 
girder,  passing  over  the  stringers,  with  the  same  rods  to 
act  as  reinforcement.  Over  this  slab  brick  or  block  or 
asphalt  pavement  may  be  laid.  The  lateral  system  on  a 
bridge  with  a  floor  of  this  sort  need  only  be  strong  enough 
to  take  care  of  lateral  forces  during  erection,  as  the  con- 
crete slab  will  give  ample  stiffness. 

SURFACE  FINISH.  Every  contract  for  concrete  work 
should  include  a  clause  requiring  that  the  exposed  surface 
be  properly  finished.  The  finish  should  be  appropriate  to 
the  nature  of  the  work.  In  some  cases  this  may  mean 
merely  a  washing  down  to  remove  dirt  and  efflorescence 
after  removal  of  forms.  An  otherwise  good  job  of  con- 
146 


creting  may  appear  very  poor  on  account  of  failure  to  treat 
the  surface  properly,  and  the  owner  may  have  to  go  to 
considerable  expense  to  improve  the  appearance  of  a  struc- 
ture .by  reason  of  failure  to  specify  the  kind  of  finish  de- 
sired. 

WATERPROOF  PLASTER.  A  mixture,  by  volume,  of  3  parts 
of  litharge,  I  part  of  glycerine,  48  parts  of  Portland  ce- 
ment, and  48  parts  of  sand  makes  a  strong,  adherent,  and 
dense  plaster,  which  will  repel  water.  Hot  paraffine  is 
sometimes  ironed  into  concrete  to  waterproof  the  surface. 
Linseed  oil,  painted  on  until  the  concrete  will  absorb  no 
more,  is  also  used  to  waterproof  concrete  that  has  not 
been  properly  made  and  lacks  density. 

WHITEWASH.  Whitewash  for  concrete  surfaces  should 
be  durable  and  adhesive.  The  following  is  recommended. 
Slake  with  warm  water,  half  a  bushel  of  lime,  covering 
it  during  the  process  to  keep  in  the  steam ;  strain  the  liquid 
through  a  fine  sieve  or  strainer :  add  a  peck  of  salt,  pre- 
viously well  dissolved  in  warm  water,  3  Ib.  of  ground  rice, 
boiled  to  a  thin  paste  and  stirred  in  boiling  hot  water,  l/2 
Ib.  of  powdered  Spanish  whiting,  and  a  pound  of  glue 
which  has  been  previously  dissolved  over  a  slow  fire;  add 
five  gallons  of  hot  water  to  the  mixture.  Stir  well  and 
let  it  stand  for  a  few  days,  covered  from  the  dirt.  Strain 
carefully  and  apply  with  a  brush  or  a  spray  pump.  It 
should  be  put  on  hot.  Coloring  matter  may  be  put  in  to 
make  various  shades. 

SOME  USES  OF  CONCRETE.  Some  of  the  more  uncommon 
situations  in  which  concrete  can  be  used  to  advantage  are 
the  following: 

For  props  in  coal  mines,  in  place  of  timber. 

To  line  steel  coal  or  ash  hoppers  or  bins. 

For  fence  posts.  These  are  usually  made  square  and 
tapered  and  have  a  reinforcing  steel  wire  near  each  cor- 
ner, these  tied  together  with  wires. 

.  For  roof  tiles  or  shingles.  These  may  be  reinforced  with 
a  wire  mesh  or  metal  lath  of  some  kind. 

To  protect  wooden  piles  in  sea  water  from  toredo.     To 

147 


accomplish  this  the  concrete  may  be  molded  into  a  cylin- 
der around  the  pile.  Steel  reinforcement  must  be  used  to 
hold  the  concrete  from  breaking  off.  Another  method  is 
to  use  concrete  half-cylinders  surrounding  the  pile,  or 
sewer  pipe  of  clay  or  concrete  if  they  can  be  threaded  over 
the  top  of  the  pile.  The  space  between  the  pile  and  the 
surrounding  cylinder  is  then  filled  with  sand.  In  the  event 
of  a  break  in  the  surrounding  cylinder  the  sand  will  run 
out  and  the  damage  can  be  detected  and  repaired. 


Estimating  Cost. 


The  cost  of  a  structure  is  a  function  of  the  number  of 
pounds  of  steel  or  cast  iron,  the  number  of  cubic  feet  or 
yards  of  masonry,  the  number  of  bricks,  the  number  of 
feet  of  board  measure,  the  number  of  square  feet  of  pav- 
ing, of  lineal  feet  of  handrailing,  etc.,  that  go  to  make  up 
the  whole.  An  estimate  of  the  cost  requires  careful  calcu- 
lating of  all  of  these  as  well  as  a  knowledge  of  a  fair  unit 
price  at  which  they  can  be  put  into  the  structure. 

Cost  estimates  must  be  based  on  unit  values.  The  ac- 
curacy of  the  estimate  will  often  depend  upon  the  particu- 
lar unit  at  which  the  estimate  starts.  Sometimes  greater 
accuracy  will  result  from  tracing  back  the  unit  cost  of  the 
raw  materials  of  manufacture :  often  such  tracing  is  pro- 
ductive of  only  confusion  with  no  increased  accuracy.  For 
example,  there  is  nothing  gained  by  analyzing  the  cost  of 
a  pound  of  steel  or  a  barrel  of  cement.  These  materials 
have  certain  prices  fixed  by  those  who  sell  them.  In  the 
matter  of  working  up  materials  there  are  also  arbitrary 
elements.  The  cost  per  unit  will  depend  upon  the  particu- 
lar plant  or  equipment  employed  and  its  fitness  to  handle 
the  work  most  economically. 

The  plant  or  equipment  needed  to  do  a  piece  of  work 
should  be  selected  with  a  view  of  the  size  of  the  work  and 
the  time  in  which  it  is  to  be  finished.  Large  equipment 
cannot,  in  general,  be  used  economically  on  a  small  job, 
and  small  equipment  cannot  be  used  economically  on  a 

148 


large  job.  The  size  of  a  concrete  plant  should  be  such 
that  its  normal  daily  capacity  is  about  equal  to  the  amount 
of  concrete  that  it  is  desired  to  turn  out  per  day.  For 
maximum  economy  a  plant  should  be  employed  continous- 
ly.  If  stops  must  be  made  to  wait  for  forms  to  be  put  in 
readiness,  or  for  other  causes,  the  concrete  will  cost  more 
than  if  the  work  of  the  concrete  mixing  can  be  carried  on 
continuously. 

For  small  concrete  jobs,  such  as  pavement  work,  hand 
mixing  is  more  economical.  Small  batches  may  be  mixed 
with  a  hoe  or  shovels  in  a  box.  Half-yard  batches  should 
be  mixed  on  a  platform  by  at  least  two  men  with  shovels. 
The  platform  may  be  made  of  a  steel  plate  or  of  boards 
placed  with  close  joints  on  a  frame. 

A  typical  gang  mixing  and  laying  one-half  cubic  yard 
batches  is  the  following:  I  foreman,  2  men  delivering 
sand  and  stone,  I  man  delivering  cement,  2  men  mixing 

2  men  delivering  concrete,  I  man  tamping.     At  $3  per  day 
for  the  foreman  and  $1.50  per  day  for  each  of  the  other 
men  the  cost  per  day  of  this  gang  is  $15.    The  gang  should 
turn  out  about  20  to  25  cu.  yds.  per  day.     This  is  a  cost 
of  75  cts.  to  60  cts.  per  cu.  yd.  for  labor. 

A  typical  gang  for  mixing  and  laying  by  hand  cubic- 
yard  batches  is  as  follows :  I  foreman,  3  men  delivering 
sand  and  stone,  I  man  delivering  cement,  4  men  mixing, 

3  men  delivering  concrete,  2  men  tamping.       The  cost  of 
this  gang  at  the  same  wages  as  above  is  $22.50  per  day. 
They  should  turn  out  about  40  cubic  yards  per  day,  making 
the  cost  of  labor  56  cts.  per  cu.  yd. 

The  above  examples  give  about  average  conditions  and 
show  the  cost  of  labor  on  hand  mixed  concrete  in  heavy 
work  where  mixing  and  laying  can  go  on  continuously. 
If  labor  is  cheap  (and  efficient)  the  unit  cost  may  be  less, 
and  vice  versa.  If  materials  can  be  deposited  for  easy 
handling,  as  when  they  are  laid  close  to  the  mixing  board 
and  need  only  to  be  measured  the  unit  cost  will  be  reduced 
accordingly,  whereas  long  hauls  or  high  lifts,  either  before 
or  after  mixing  will  add  to  the  cost  very  materially.  If 
149 


the  gang  cannot  be  continuously  employed,  costs  may  be 
two  or  three  times  as  much  as  the  above.  Concrete  de- 
posited in  narrow  forms  will  also  cost  more  per  cu.  yd. 
than  in  massive  work. 

With  mechanical  mixers  the  cost  of  mixing  concrete  will 
be  less  than  by  hand  mixing,  though  the  extra  cost  of 
skilled  workers  to  run  the  engine  and  mixer  helps  to  bal- 
ance the  costs.  Batch  mixers  should  turn  out  about  20 
batches  per  hour. 

Current  prices  for  which  similar  work  is  being  done  in 
localities  situated  about  the  same  distance  from  the  source 
of  supply  afford  a  sound  basis  upon  which  to  gage  the 
cost  of  work.  It  is  best  for  the  engineer  not  engaged  in 
the  estimating  of  cost  to  the  contractor  or  manufacturer 
to  use  as  a  base  the  unit  cost  of  work  in  place,  rather  than 
to  analyze  the  elements  that  go  to  make  up  that  cost, 
such  as  material,  labor,  freight,  hauling,  profit,  etc.  The 
contractor's  profit  is  an  elastic  factor,  depending  upon  the 
size  of  the  work,  the  risk,  and  many  other  considerations. 
The  cost  of  manufacture  is  variable.  Some  shops  can 
make  heavy  work  cheaper  than  others,  while  others  can 
handle  light  work  more  economically.  It  is  not  the  pur- 
pose here  to  analyze  the  cost  in  shops  and  mills,  so  much 
as  to  give  more  general  data  for  determining  the  probable 
cost  of  ordinary  building  and  bridge  work,  as  well  as  to 
point  out  some  of  the  special  cases  where  costs  are  apt  to 
be  more  or  less  than  the  average.  Average  costs  will  pre- 
vail near  the  railroads  and  within  radii  of  50  or  100  miles 
of  the  commercial  centers.  Freight  rates  average  about 
%  to  one  and  one-half  cents  per  ton-mile.  Long  pieces 
requiring  several  cars  and  not  weighing  enough  to  load 
them  to  their  normal  capacity  will  cost  more  per  ton  than 
materials  that  can  be  shipped  in  full  car  loads.  Partial 
carloads  are  charged  at  a  minimum  car  load  rate,  say  one- 
half  of  the  capacity  of  the  car.  Where  more  than  one  car 
is  required,  one  car  is  charged  at  this  minimum  rate  and 
each  other  car  at  one-half  of  this  amount,  if  the  actual 
weight  of  the  material  shipped  is  not  over  that  total. 

150 


Hauling  under  ordinary  conditions  costs  about  50  cents 
per  ton  for  structural  material. 

The  actual  cost  of  hauling  crushed  stone  i%  miles  in 
some  macadam  paving  was  found  to  be  26.6  cts.  per  ton 
when  drawn  from  the  crusher  bins  and  31  cts.  per  ton  when 
drawn  from  the  piles.  The  contract  price  was  32^  cts.  per 
ton. 

The  hire  of  a  dumping  wagon  and  team  and  driver  is 
about  4  dollars  per  day:  that  of  a  horse  and  cart  and 
driver  is  about  three  dollars  per  day. 

The  actual  cost,  with  stone  free  at  the  quarry,  of  lay- 
ing macadam  pavement  (  5"  layer  large  sized  stone,  rolled ; 
2^/z"  to  3"  layer  of  medium  sized  stone,  sprinkled  and 
rolled ;  about  %"  of  fine  screenings,  sprinkled  and  rolled) 
was  42  cents  per  square  yard.  The  average  weight  of 
stone  was  .3  tons  per  sq.  yd.  (Eng.  News,  Oct.  8,  1903). 

The  actual  cost  of  quarrying  and  crushing  stone  in  the 
above  mentioned  work  was  42  cts.  per  ton ;  in  which  coal 
delivered  cost  4  dollars  per  ton,  a  driller  $1.75  per  day,  help- 
er $1.50  per  day,  engineman  $2  per  day. 

The  cost  of  mixing  materials  and  laying  the  same  in 
making  the  Buffalo  breakwater  was  as  follows : 

Laying   Materials 17.4  cts.  cu.  yd. 

Mixing  Materials   12.9  cts.  cu.  yd. 

Placing  mixed  materials   14.6  cts.  cu.  yd. 

Total         44.9  cts.  cu.  yd. 

Sometimes  the  gravel  and  sand  for  a  piece  of  work  can 
be  found  at  or  near  the  site,  thus  greatly  reducing  the  cost 
of  concrete  made  of  the  same. 

Bricks  may  be  hauled  direct  from  the  works  without  the 
expense  of  loading  and  unloading  on  cars. 

Extra  hazardous  work  should  have  something  added  to 
the  estimated  cost  to  allow  for  the  risk  taken  by  the  con- 
tractor. Work  that  must  be  finished  in  a  short  time  should 
have  the  estimate  increased,  especially  if  a  penalty  attaches 
for  failure  to  complete  by  a  specified  time.  If  the  season 
is  a  poor  one  for  the  class  of  work,  still  more  expense  is 
liable  to  be  incurred.  Erecting  of  bridges  over  streams  in 

151 


flood  time  may  be  attended  by  serious  difficulties  and  ex- 
pensive delays. 

Large  contracts,  as  a  rule,  cost  less  per  unit  than  small 
ones.  The  placing  and  removing  of  the  contractors  plant 
on  a  job  often  requires  considerable  time.  If  the  magni- 
tude of  work  does  not  justify  bringing  labor  saving  ma- 
chinery to  the  site,  the  extra  labor  will  make  the  smaller 
job  more  expensive.  Large  orders  of  materials  may  be 
placed  at  lower  rates  than  small  ones. 

Where  labor  is  the  principal  item  of  cost  in  any  work, 
less  certainty  can  be  expected  in  the  estimate  of  the  cost, 
and  little  agreement  between  prices  bid  by  contractors; 
whereas  materials  that  are  regularly  manufactured  should 
vary  but  little  in  cost. 

There  are  some  general  rules  that  will  be  found  very 
useful  in  making  a  rough  estimate  of  the  cost  of  structures 
and  checking  against  large  errors  in  more  careful  esti- 
mates. The  cost  per  square  foot  of  area  covered  by  a 
building  having  practically  one  floor  will  be  nearly  con- 
stant for  different  sizes  of  buildings  of  the  same  class. 
Higher  buildings  will  have  a  cost  per  cubic  foot  nearly 
constant  for  a  given  class  of  building.  For  ordinary  lengths 
of  spans  the  cost  of  reinforced  concrete  bridges  per  square 
foot  of  floor  does  not  vary  much. 

The  cost  per  square  foot  of  the  area  covered  by  buildings 
of  the  World's  Columbian  Exposition  for  nine  of  .the 
principal  buildings  varied  between  75  cents  and  $2.35,  and 
averaged  about  $1.50.  The  Administration  building  cost 
$9.18  per  square  foot.  The  cost  per  square  foot  under 
roof  of  eleven  of  the  principal  buildings  of  the  Louisiana 
Purchase  Exposition  varied  between  61  cents  and  $1.49 
with  an  average  of  $1.12.  Festival  Hall  cost  $5.23  per  sq. 
ft.  Fine  Arts  Building  (central  building)  cost  $9.88  per 
sq.  ft.,  U.  S.  Gov't.  Building  cost  $2.31  per  sq.  ft.  The 
eleven  buildings  at  St.  Louis  have  timber  framework.  The 
Chicago  buildings  had  steel  frames.  The  Fine  Arts  Build- 
ing at  St.  Louis  is  permanent  and  fire-proof.  The  U.  S. 

152 


Gov't.  Building  has  steel  arches.  The  cost  of  the  sterl 
work  alone  was  65  cents  per  sq.  ft. 

The  cost  per  square  foot  of  floor  of  what  is  probably 
the  longest  stone  arch  in  the  world;  namely,  the  bridge 
at  Plauen,  Saxony  with  a  span  of  295.2  feet,  was  $4.65. 
Low  cost  of  labor  and  availability  of  stone  close  to  the 
bridge  made  its  cost  much  lower  than  such  a  bridge  could 
ordinarily  be  built  for  (Eng.  News,  Jan.  28,  1904). 

Fern  Hollow  Bridge  at  Pittsburg,  Pa.,  cost,  including 
the  masonry  $4.06  per  sq.  ft.  of  floor.  This  is  a  plate  gir- 
der arch  with  viaduct  approaches.  The  arch  span  is  195 
feet.  It  was  estimated  that  a  stone  arch  bridge  would 
have  cost  nearly  three  times  as  much.  (Eng.  News,  Feb. 
26,  1903). 

The  cost  of  a  double  track  stone  arch  railroad  bridge 
of  64-foot  spans  at  Watertown,  Wis.  was  $4.35  per  sq.  ft., 
including  removal  of  old  bridge.  (See  Eng.  News,  Vol. 
49*  P-  266). 

The  cost  of  the  P.  R.  R.  Co.'s  four-track  stone  arch 
bridge  at  Rockville,  Pa.  was  $5.03  per  square  ft. 

Following  are  the  approximate  costs  of  reinforced  con- 
crete arch  bridges  per  square  foot  of  roadway  and  side- 
walk, end  to  end  of  abutments : — 

Bridge  at  Dayton,  O.,  Spans  69  to  88  ft.  Pavement  of 
bituminous  macadam.  Assuming  abutments  20  ft.  each, 
cost  per  sq.  ft.  =  $3.63  (Eng.  News,  May  19,  1904). 

Bridge  at  Dayton,  O.,  Spans  80  to  no  ft.  Cost,  includ- 
ing provision  for  temporary  traffic  and  removal  of  old 
bridge,  $3.63  per  sq.  ft.  (R.  R.  Gazette,  May  4,  1904). 

Bridge  at  Forest  Park,  St.  Louis,  Span  45  ft.  Macadam 
pavement  on  roadway.  Cost  per  sq.  ft.  $3.63.  (Eng.  News, 
June  n,  1903). 

Bridge  at  Laibach,  Austria.  Span  108  ft.  Cost  $32,000 
($4.14  per  sq.  ft.)  The  metal  work  of  this  bridge  cost 
about  $6,000  and  the  ornamental  work  $2,000.  (Eng.  News, 
July  1 6,  1903). 

Bridge  at  Brooklyn,  N.  Y.  Skew  arch.     Cost  $2.85  per 

153 


sq.  ft.  Contains  91,360  Ibs,  of  steel  and  1300  cu.  yds.  of 
concrete.  (Eng.  News,  Dec.  30,  1903). 

Bridge  at  Waterloo,  Iowa.  Seven  spans  each  72  ft.  Cost 
per  sq.  ft.  $1.65.  This  does  not  include  floors  and  pave- 
ments. Bridge  contains  7200  bbls.  Portland  cement,  5000 
cu.  yds.  crushed  rock,  3000  cu.  yds.  sand,  no  tons  of  steel 
ribs,  6,000  cu.  yds.  of  spandrel  filling.  (Eng.  Record,  Feb. 
13,  1904). 

Bridge  at  Des  Moines,  Iowa.  Spans  100  ft.  Spandrel 
walls  and  arch  ring  faced  with  brick.  Cost  per  sq.  ft. 
$4.48.  (Eng.  News,  May  14,  1903). 

Bridge  at  Topeka,  Kan.  Longest  span  125  ft.  Cost  $4.51 
per  sq.  ft.  (Eng.  News,  Apr.  2,  1896). 

Bridges  at  Niagara  Falls.  Cost  of  two  bridges  $4.60 
per  sq.  ft.  (Eng.  Record,  Feb.  16,  1901). 

Bridges  in  Porto  Rico.  One  bridge  having  i — i2O-ft. 
and  2 — zoo- ft.  spans  and  rather  high  piers  cost  $8.17  per 
sq.  ft.  and  one  having  3 — 7o-ft.  spans  cost  $5.29  per  sq.  ft. 
(Eng.  News,  Aug.  i,  1901) 

Bridge  at  Washington  Street,  Dayton,  O.,  about  $3.30 
per  sq.  ft.  (Eng.  Record,  Mar.  2,  190?). 

Bridge  at  Sandy  Hill,  N.  Y.,  $2.43  per  sq.  ft.  (Eng.  Rec- 
ord. May  4,  1907.) 

Bridge  at  Jacksonville,  $3.00  per  sq.  ft.  (Eng.  Record, 
May  18,  1907). 

Bridge  at  Mishawaka,  $3.82  per  sq.  ft.  (Eng.  Record,  July 
7,  1906.) 

Bridge  at  South  Bend.  $3.32  per  sq.  ft.  (Eng.  Record, 
July  28,  1906.) 

Bridge  at  Philadelphia,  $6.85  per  sq.  ft.  (Eng.  Record, 
Nov.  17,  1906.) 

Bridge  near  Goshen,  O.,  $4.67  per  sq.  ft.  (Eng.  Record, 
Mar.  30.  1907.) 

Bridge  over  Rock  Creek,  Washington,  D.  C.  (Boulder- 
faced  span,  illustrated  in  this  book),  $5  per  sq.  ft.  (Eng. 
Record,  Vol.  46,  p.  151.) 

The  cost  in  1903  of  a  large  reinforced  concrete  factory 

154 


building  was  6.4  cts.  per  cu.  ft.  This  was  for  the  building 
alone,  not  including  plumbing  or  furnishings. 

•Mr.  H.-G.  Tyrrell  (R.:R.  Gazette,  Vol.  37,  No.  i8)  made 
comparative  estimates  of  a  large  factory  building  designed 
to  carry  100  Ibs.  per  sq.  ft.  of  live  load  (six  stories  and 
basement),  and  found  that  a  building  of  heavy  wooden 
interior  construction  with  brick  floors,  and  cast  iron  col- 
umns in  the  lower  two  tiers  would  cost  6.2  cts.  per  cu.  ft. 
or  83  cts.  per  sq.  ft.  of  area  of  floors;  the  same  building 
with  concrete  steel  floors  on  a  steel  frame  work  would 
cost  10.2  cts.  per  cu.  ft.  or  $1.36  per  sq.  ft.  of  area  of 
floors.  This  did  not  include  furnishings  or  stairs. 

The  cost  of  a  reinforced  concrete  power  building  per  cu. 
ft.  above  ground  was  7.7  cts.  (See  description,  Eng.  Rec- 
ord, Apr.  15,  1905,  p.  438.)  The  total  cost  of  this  building 
was  $225,000. 

The  cost  of  a  brick  building  with  slate  roof  on  timber 
will  probably  be  from  8  to  14  cents  per  cubic  foot  of  its  vol- 
ume. 

The  cost  of  a  mill  building  with  sides  and  roof  of  cor- 
rugated iron  will  probably  be  from  75  cents  to  $1.50  per 
square  foot  of  plan. 

The  cost  of  apartment  buildings  and  department  stores 
as  usually  constructed  will  be  from  20  to  30  cents  per  cubic 
foot  of  volume. 

Office  buildings  will  usually  run  from  30  to  60  cents  per 
cubic  foot. 

City  dwellings  will  run  from  10  to  30  cents  per  cubic  foot. 

Brick  veneer  dwellings  will  cost  about  8  cents  per  cubic 
foot. 

Window  and  door  frames  as  ordinarily  made  for  mill 
buildings  cost  about  25  cents  per  square  foot  in  place  es- 
timating the  dimensions  out  to  out  of  frames.  Galvanized 
iron  louvres  of  No.  18  iron  cost  about  the  same. 

The  cost  of  furnishing  clips  and  rivets  and  putting  up 
corrugated"  iron  is  about  "$2.00  per  square  of  100  square 
feet. 

Erection  of  plain  structural  work  costs  9  to  10  dollars 
155 


per  ton;  of  frame  work  of  office  buildings  10  to  12  dollars 
per  ton;  of  mill  buildings  n  to  15  dollars  per  ton.  Com- 
plicated work  of  many  small  parts  and  light  tonnage,  such 
as  angles  and  tees  for  roof  tile,  may  run  as  high  as  28  to 
30  dollars  per  ton  to  erect.  Bridge  truss  work  will  cost 
15  to  20  dollars  per  ton.  These  figures  include  furnish- 
ing falsework,  also  the  painting. 

The  painting  of  structural  work  costs  about  one  dollar 
per  ton  for  each  coat. 

The  driving  of  field  rivets  costs  from  5  cents  to  20  cents 
each,  depending  upon  the  accessibility  of  the  rivets  and 
the  number  of  times  that  scaffolds  must  be  moved  in  a  day. 
A  riveting  gang  costs  about  18  dollars  a  day.  For  ordin- 
ary work  12  cents  per  rivet  is  a  good  average. 

The  hire  of  an  engine  and  derrick  is  about  30  dollars 
per  week.  That  of  an  engine  and  concrete  mixer  is  about 
the  same.  This  does  not  include  any  men  to  operate  the 
same. 

The  hire  of  a  road  roller  with  coal  and  operator  is  about 
12  dollars  per  day. 

The  hire  of  a  work  train  and  crew,  coal,  etc.,  is  about 
$22  per  day. 

The  cost  of  galvanizing  structural  work  is  about  twenty 
dollars  a  ton. 

The  cost  of  corrugated  steel  roofing  or  siding  per  square 
of  100  square  feet,  at  3^  cents  per  pound  for  material  and 
$2.25  per  square  for  erection  and  painting  is  about  $11.75 
for  No.  18  and  about  $9.00  for  No.  20.  Galvanized  roofing, 
at  one  cent  extra  for  galvanizing  would  cost  about  $14.50 
for  No.  18  and  about  $11.00  for  No.  20  per  square  erected. 

The  cost  of  concrete-steel  roofing  on  1 5-foot  spans  is 
about  25  to  30  cents  per  square  foot,  exclusive  of  covering. 
Concrete-steel  floors  for  ordinary  loads  on  spans  8  to  10 
ft.  cost  about  the  same.  Heavy  floors  cost  30  to  40  cents 
per  sq.  ft.  Cement  finish  on  floors  costs  7  to  10  cents  per 
sq.  ft. 

The  cost  in  1903  of  a  54  inch  self-supporting  steel  stack 
no  ft.  high  of  5-16",  %",  and  3-16"  metal,  including  lad- 

156 


der,  painted  on  outside,  with  base  casting,  but  not  anchor 
bolts  or  foundation,  was  $1,200.  Breeching  of  3-16"  metal, 
5  ft.  in  diameter  or  oblong  and  same  area  cost  $9.00  per 
lineal  foot. 

The  cost  in  1902  of  a  stack  10  ft.  inside  diameter  and 
180  ft.  high,  of  porous  brick,  was  $7,375,  not  including 
foundation.  A  125-ft.  x  6-ft.  porous  brick  stack,  includ- 
ing foundation,  will  cost  about  $4,000.  The  cost  in  1903 
of  a  reinforced  concrete  stack  150  ft.  high,  6  ft.  inside 
diameter,  including  foundation,  was  $3,800.  The  contract 
price  in  1907  of  a  reinforced  concrete  stack  166  ft.  high, 
8  ft.  inside  diameter,  was  $4,100. 

The  cost  of  a  n8,ooo-gallon  concrete-steel  stand  pipe, 
with  enclosing  tower,  at  Hull,  Mass,  was  about  $12,000. 
(See  Eng.  News,  Vol.  52,  p.  596.) 

Mr.  H.  G  Tyrrell,  in  R.  R.  Gazette,  Dec.  30,  1904,  shows 
that  the  cost  of  the  parts  of  single  track  steel  trestle  for 
£50  loading,  towers  30  ft.  between  bents,  at  3^5  cts.  per 
Ib.  for  girders,  4  cts.  per  Ib.  for  bents  and  bracing,  and 
$10  per  cu.  yd.  for  concrete,  are  as  follows : 

Length  Cost  of  Steel  Trestle  120  Ft.  High  per  lin.  ft. 
intermediate  j  |  j  Traction  |  ] 

Span  Spans        Bents     Bracing        Piers        Total 

30         $15.15    $45-2    $15.2     $12.0     $87.55 

60  21.77  39.2  13.0  8.0  82.57 

100  39.09  32.0  10.8  5.5  87.39 

In  Proceedings,  Am.  Ry.  Eng.  M.  of  W.  Asso.  Vol.  2, 
p.  139  it  is  stated  that  the  cost  of  ballasted  trestle  on  the 
A.  T.  &  S.  Fe  Ry.,  2  examples,  averaged  $12.66  per  lin. 
ft.  divided  as  follows :  treated  piles,  $5.02 ;  lumber,  $5.01 ; 
bolts,  $.21;  cross  ties,  $.24;  ballast,  $.285;  labor  (all  kinds), 
$1.89;  creosote,  $.005. 

Mr.  J.  C.  Bland,  in  1891,  found  the  estimated  contract 
price  of  single  track  timber  trestle  was,  in  round  numbers, 
nearly  equal  in  dollars  per  lineal  foot  to  one-half  of  the 
height  of  trestle  in  feet  out  to  out  of  cap  and  sill.  In  this 
the  floor  deck  alone  was  $4.22  per  ft.  of  track  and  piles 
$3  each;  both  increased  by  20%  for  the  contractor's  profit. 

157 


Timber  in  place  was  estimated  at  $52  to  $55  per  M.  B.  M., 
contract  price. 

A  number  of  examples  of  the  cost  of  railroads  are 
given  in  R.  R.  Gazette,  Sept.  7,  and  Oct.  26,  1906,  as  fol- 
lows:  ist  case.  No  tunnels,  few  bridges,  along  river,  con- 
siderable cut  and  fill,  single  track,  $26,300  per  mile.  2d 
case.  Along  river,  heavy  cuts,  some  bridges,  single  track, 
$37,014  per  mile.  3d  case.  Cuts  and  fills,  bridges,  tun- 
nels, single  track,  $60,628  per  mile.  4th  case.  Heavy  cross- 
ings, double  track,  $76,336  per  mile.  5th  case.  Heavy  cross- 
ings, double  track,  $105,186  per  mile.  6th  case.  Detour 
around  large  city,  double  track,  $50,000  per  mile.  In  the 
foregoing  the  cost  includes  preliminary  surveys,  clearing 
right  of  way,  roadbed,  ties,  rails,  ballast,  side  tracks,  but 
does  not  include  real  estate,  stations  equipment,  or  signals. 

Following  is  a  list,  alphabetically  arranged,  giving  prices 
of  various  materials  and  work,  to  be  used  as  a  guide  in 
estimating  the  cost  of  structures.  These  are  taken  largely 
from  current  price  lists  and  contract  prices,  as  published 
in  engineering  journals,  and  in  general  indicate  prices 
prevailing  in  1904  to  1907. 

ASPHALTUM:  Ventura  and  other  California  asphalts, 
$20  to  $23  per  ton  at  New  York;  Trinidad  refined,  $22  to 
$25  per  ton ;  Venezuela  asphalt,  $25  to  $60  per  ton ;  Ber- 
muda asphalt,  $25  to  $35. 

BRICK:  At  yards,  per  thousand,  common  soft,  $5  to 
$7;  hard  $7  to  $9;  vitrified  (hard  burned),  paving,  com- 
mon, $8  to  $12,  special,  $15  to  $20;  select  red,  not  pressed, 
$8  to  $10,  pressed,  $14  to  18;  Roman,  $30;  fire  bricks,  $14. 
Freight  on  bricks  is  about  $2  per  thousand  for  50  mile  run. 

BRONZE :     Phosphor,  in  place,  abt.  40  cts.  Ib. 

CAST  IRON :     Pig  Iron,  $19  to  $22  per  long  ton. 

Cast  iron  counterweights,  iVz  to  2  cts.  per  Ib.  delivered. 

Cast  iron  pipe,  $33  to  $38  per  ton  delivered;  laid,  $38 
to  $45  per  ton. 

Standard  and  plain  castings,  21/fc  to  3%  cts.  per  Ib.  in 
place.  Special  castings,  large  orders,  3  to  5  cts.  per  Ib. 
in  place;  small  orders  5  to  10  cts. 

158 


CEMENT:     Portland  $1.50  to  $2.00  per  bbl.,  400  Ibs. 

Rosendale,  So  cts.  to  $i  per  bbl.,  300  Ibs. 

Large  users  of  Portland  cement  pay  less  than  $1.50  per 
bbl.  for  domestic  brands.  On  small  orders  freight  and 
handling  increase  the  cost. 

CEMENT  FINISH:  Portland,  mortar  %  in.  thick  50 
to  80  cts.  per  sq.  yd. 

CLAY :  Fireclay,  dry  powder  $1.50  ton  delivered  on 
cars;  calcined  fireclay,  $3  to  $4  ton. 

For  puddle  $1.50  cu.  yd.  delivered. 
CONCRETE:     Natural  cement,  $3  to  $5  cu.  yd.  in  place. 

Portland  cement,  in  large  mass,  easily  deposited,  $4  to  $7 
cu.  yd.  Walls  requiring  difficult  forms,  $6  to  $8  cu.  yd. 
Tunnels,  etc.  $10  to  $12  cu.  yd. 

The  cost  of  1:3:6  Portland  cement  concrete  may  be 
analyzed  as  follows: 

i  cu.  yd.  broken  stone $2.00 

l/2  cu.  yd.  sand 50 

I  bbl.  cement  , , 2.00 

Mixing  and  depositing  .50 

Total  $5.00 

This  is  with  the  use  of  a  mechanical  mixer.  Hand  mix- 
ing would  probably  cost  from  70  cts.  to  $1.25  per  cu.  yd. 

For  detailed  information  on  the  cost  of  concrete  struc- 
tures on  the  N.  C.  &  St.  L.  R.  R.  see  paper  by  H.  M.  Jones, 
published  in  part  in  the  R  R.  Gazette,  Oct.  21,  1904.  The 
cost  to  the  R.  R.  Co.  per  cubic  yard  for  culverts  and  walls 
run  about  $6  to  $7.  Two  examples  are  a  little  over  $9. 

Reinforced  concrete,  including  steel,  usually  costs  from 
$10  to  $20  per  cu.  yd.  Concrete  should  be  estimated  at  $5 
to  $10  per  cu.  yd.  in  place,  steel  at  about  2.5  cts  per  Ib.  in 
place  (plain  structural  steel),  forms  5  to  10  cts.  per  sq. 
ft.  The  unit  cost  of  concrete  will  depend  upon  the  diffi- 
culty of  handling  and  placing. 

COPPER:     14  to  15  cts.  Ib. 

CURB:  Cement  and  sand,  1:3,  25  to  50  cts.  per  lineal 
foot,  about  Vz  ct.  per  sq.  in.  of  section  per  lineal  foot,  in 
place. 

159 


Sandstone  and  limestone,  50  cts.  to  $i  per  lineal  foot,  in 
place. 

Bluestone,  $i  to  $1.50  per  lineal  ft.  in  place. 

Granite,  $i  to  $2.50,  lin.  ft.  in  place. 

Curved  curbs  in  stone  20%  to  100%  extra. 

Resetting  curb  10  to  50  cts.  per  ft. 

DREDGING :  Soft  material  12  to  30  cts.  per  cu.  yd. ; 
gravel  and  hard  material  30  cts.  to  $i  cu.  yd.  In  Eng. 
News,  Sept.  20,  1906,  a  report  is  given  of  some  dredging 
done  by  U.  S.  Govt.  Engineers  with  hydraulic  dredges 
(New  York  Harbor)  which  cost  only  5.274  cts.  per  cu.  yd. 

EXCAVATING:  In  earth,  large  masses,  above  water, 
25  to  50  cts.  cu.  yd.,  below  water,  for  piers,  $i  to  $5  cu.  yd. ; 
in  trench,  earth,  50  cts.  to  $i  cu.  yd. ;  loose  rock,  $i  to  $2 
cu.  yd. ;  hard  rock,  $i  to  $3  cu.  yd. 

Steam  shovel  work  costs  about  12  to  20  cts  per  cu.  yd. 
In  Eng.  Record,  Vol.  54,  p.  732,  some  data  are  given  from 
a  paper  by  Mr.  John  C.  Sessor  on  steam  shovel  work  on 
the  C.  B.  &  Q.  Ry.  On  one  job  of  251,711  cu.  yds.  1,104 
cu.  yds.  were  moved  per  lo-hr.  shift.  The  cost  was  as 
follows :  equipment,  i  cent ;  steam  shovel  service,  8.9  cents ; 
temporary  trestle,  3.6  cents ;  track  and  track  work,  5  cents : 
supervision  and  engineering  0.2  cents;  total,  18.7  cents, 
all  per  cubic  yard.  On  another  job  of  188,240  cu.  yds.  946 
cu.  yds.  were  moved  per  lo-hr.  shift.  The  cost  was  as 
follows:  equipment,  iVz  cents;  steam  shovel  service,  9.6 
cents;  temporary  trestle,  3.1  cents;  track  and  track  work, 
4.2  cents;  supervision  and  engineering,  0.3  cents;  total, 
18.7  cents,  all  per  cubic  yard. 

The  I.  C.  R.  R.  estimates  excavating  in  earth,  in  jobs 
below  50,000  cu.  yds.,  to  cost  25  cts.  per  cu.  yd.,  and  in 
larger  jobs,  20  cts.  per  cu.  yd.  adding  in  both  cases  one 
cent  per  cu.  yd.  per  loo-ft.  haul. 

A  committee  report  of  the  Roadmaster's  and  Maintain- 
ance-of-Way  Asso.,  published  in  the  R.  R.  Gazette  of  Oct. 
31,  1904,  and  in  Eng.  News  of  Oct.  27,  1904,  gives  the  fol- 
lowing as  the  cost  of  ditching  cuts  and  widening  embank- 
ments. 

160 


By  wheelbarrows :  12.2  cts.  per  cu.  yd.  plus  31  cts.  per 
cu.  yd.  per  1000  ft.  haul  for  common  loam  or  7.3  cts.  extra 
in  bad,  wet  material. 

By  push  cars:  19.1  cts.  per  cu.  yd.,  where  material  is 
unloaded  by  shovel,  or  15.9  cts.  where  unloaded  by  dump- 
ing box,  or  similar  arrangement,  plus  33.4  cts.  per  cu.  yd. 
per  5,000  ft.  haul. 

By  machine  ditcher:  22  to  30  cts.  per  cu.  yd.,  the  latter 
figure  being  for  a  1 5-mile  haul  in  loam.  In  wet  or  bad 
material  add  about  4.5  cts.  per  cu.  yd. 

The  same  report  places  the  cost  of  team  work  with 
scrapers  at  14  to  25  cts.  per  cu.  yd.,  and  of  ditching  by 
casting,  in  fair  digging,  where  one  cast  will  place  the  ma- 
terial in  suitable  final  location,  at  10  cts.  per  cu.  yd.  Much 
valuable  information  is  given  in  this  report. 

FENCE:     Board,  50  cts.  to  $1.50  per  ft. 

FILLING:  Earth,  material  at  hand,  20  cts.  to  50  cts. 
cu.  yd. 

FLAG  STONE :    In  place  $i  to  $3  sq.  yd. 

FORMS:  Allow  5  to  10  cts.  per  sq.  ft.  for  concrete 
forms,  depending  on  whether  lumber  is  dressed  or  not  and 
on  number  of  times  it  can  be  used. 

FRENCH  DRAIN :    50  cts.  to  $i  lin.  ft. 

FUEL:  Hoisting  engines,  etc.  Allow  l/3  ton  of  coal 
per  10  horse  power  per  10  hr.  shift.  (Gillette.) 

GRAVEL:  In  bank,  15  to  20  cts.  cu.  yd,  f.  o.  b.  cars 
35  to  40  cts.  cu.  yd.,  freight  for  50-mile  run,  about  75  cts. 
cu.  yd.,  hauling,  25  to  50  cts.  cu.  yd.  Usual  price  delivered 
about  $i  cu.  yd. 

LIME:  Common,  bbl.  (250  Ibs.)  80  cts.,  finishing  $i ; 
per  ton  at  works.  $3.75,  delivered,  $6. 

LEAD :     Pig,  about  4.6  cts.  Ib. ;  lead  pipe  about  5  cts.  Ib. 

MASONRY:  Rubble,  dry,  $2  to  $5  cu.  yd.,  in  mortar, 
$3  to  $8  cu.  yd.  Coursed  rubble,  large  stones,  $5  to  $8. 

Brick,  common,  $6  to  $10  cu.  yd.,  good,  $10  to  $15  cu. 
yd.  Laying  brick,  $2  to  $3  cu.  yd.  Cost  of  lime  mortar 
per  cu.  yd.  of  brick  work  about  60  cts.,  of  cement  mortar 
$i  to  $2. 

161 


On  the  basis  of  $7.25  per  M.  for  red  brick,  $2.50  per  bbl. 
for  cement,  $1.25  per  bbl.  for  lime,  $1.25  per  cu.  yd.  of 
sand,  assuming  a  mason  at  65  cts.  per  hr.  with  help  at 
37%  cts.  per  hr.  to  lay  1,200  bricks  in  8  hrs.,  a  brick  wall 
13  ins.  thick  will  cost  about  40  cts.  per  superficial  foot. 
With  pressed  brick  face  the  cost  will  be  about  50  cts.  per 
superficial  foot. 

Bridge  pier,  sandstone  or  limestone,  $8  to  $12  cu.  yd. 

Ashlar,  sandstone  or  limestone,  $12  to  $20  cu.  yd.,  gran- 
ite, $20  to  $30  cu.  yd. 

Dressed  bluestone,  for  steps  etc.,  $i  to  $2  cu.  ft. 

MINERAL  WOOL:  Slag,  ordinary,  sh.  ton,  $19;  se- 
lected, $25;  rock,  ordinary,  $32;  selected,  $40. 

PAINT:     Prepared,  $i  to  $1.50  gallon. 

PAVING:  Asphalt — In  44  cities  in  North  America  the 
cost  of  asphalt  paving  including  4  to  6  ins.  of  concrete, 
I  to  i%  ins.  of  binder,  and  iVz  to  2  ins.  of  surface,  in  1900 
varied  between  $1.43  and  $3.25  per  sq.  yd.  (See  Eng.  Rec- 
ord, Vol.  43,  No.  8.)  It  is  estimated  that  the  cost  of  guaran- 
tee for  the  first  five  years  is  3  cts.  per  yard  and  for  the  sec- 
ond five  years  is  15  cts.  per  yard.  The  congresional  ap- 
propriation bill  allowed  $1.80  per  sq.  yd.  to  be  paid  for  as- 
phalt pavements  in  Washington,  D.  C.  (Eng.  News,  Aug. 

13.  1903-) 

Asphalt  block,  $2  to  $2.50  sq.  yd. 

The  division  of  the  cost  of  asphalt  pavement  is  about 
as  follows:  2%"  of  surface,  67  cts.  sq.  yd.;  2"  of  binder 
13  cts.  sq.  yd.;  6"  of  Portland  cement  concrete  $i.  Total 
$1.80  sq.  yd. 

Brick,  work  only,  15  to  20  cts.  sq.  yd. 

Brick,  4"  of  brick  on  3"  of  sand,  65  to  85  cts.  sq.  yd. ; 
4"  of  brick  on  6"  of  natural  cement  concrete  and  i1/^"  cush- 
ion of  sand,  $1.20  to  $1.60  sq.  yd.;  sidewalks,  2"  of  brick 
on  sand  50  to  80  cts.  sq.  yd. 

Cobble  stone,  80  cts.  sq.  yd. 

Concrete  sidewalks,  finished  with  mortar  of  sand  and 
cement,  granite  screenings  and  cement,  etc.  10  to  25  cts. 
sq.  ft.  Mortar  finish  alone  5  to  15  cts.  sq.  ft. 

162 


A  common  contract  price  for  concrete  sidewalks,  small 
jobs,  is  15  to  20  cts.  per  sq.  ft.  Large  paving  work  can  be 
done  at  an  actual  cost  of  about  10  cts.  per  sq.  ft. 

Macadam,  stone  free  at  quarry,  8"  depth,  40  to  50  cts. 
sq.  yd. ;  including  cost  of  stone,  8"  depth,  60  to  90  cts.  sq. 
yd.,  12"  depth,  90  cts.  to  $1.30  sq.  yd. 

Stone  blocks  on  broken  stone  base,  $1.50  to  $2  sq.  yd. 
Stone  blocks  on  concrete  base  $2  to  $3.50  sq.  yd. 
Wooden  blocks — 4  in.   creosoted  yellow  pine  blocks  on 
one  inch  of  sand  over  6  in.   of  natural  cement  concrete 
$2.25  to  $2.35  per  sq.  yd.     Cost  of  4"  creosoted  yellow  pine 
blocks  f.  o.  b.  cars  about  $1.70  per  sq.  yd. 

The  following  analyses  of  the  cost  of  brick  and  stone 
block  paving  are  taken  from  Engineering  News,  July  24, 
1902. 

"The  following  is  a  summary  of  the  cost  of  paving  with 
brick  laid  on  edge,  wages  being  25  cts.  per  hour  for  pav- 
ers and  15  cts.  for  laborers :  Cost  per  sq.  yd. 

57  "pavers"  at  $10  per  M $0.57 

Hauling  1%  miles  over  earth  roads 06 

Laying  pavers,  including  labor  of  grouting 08 

0.18  cu.  ft.  =  1-150  cu.  yd.  of  grout* 05 

1-36  cu.  yd.  sand  cushion  at  $1.08  a  cu.  yd .03 

Plank  to  protect  concrete 01 


Total  net  cost $0.80 

Add  about  19%  for  profit 15 

Contract  price  $6-95 

*  I  Portland  to  2  sand. 

'To  this,  of  course,  must  be  added  the  cost  of  grading 
and  cost  of  concrete  foundation. 
On  block  paving  "we  have  for  the  total  labor  cost : 

Per  sq.  yd. 
Loading  and  unloading  inclusive  of  lost  team  time  $0.10 

Hauling  I  mile .05 

Distributing  blocks  03 

Laying 06 

163 


Filling  joints 06 

Foreman  at  40  cts.  per  hr.,  30  sq.  yds 013 

2  water  and  errand  boys 007 


Total  labor $0.30 

"Cost  of  Medina  Block  Pavement. 

Per  sq.  yd. 

1/3  cu.  yd.  street  excavation  $0.15 

6-in.  concrete  foundation 50 

1-18  cu.  yd  sand  cushion  in  place  at  $1.08 06 

Medina  block  (6  in.)  f.  o.  b.  Albion,  N.  Y 1.15 

Freight  to  Rochester 07 

Unloading,  hauling  and  laying 30 

1.5  gallons  tar  at  10  cts.  a  gallon 15 

1-50  cu.  yd.  sand  for  joints 02 


Total  $2.40 

Add  for  contractor's  profit 25 


Total  cost $2.65 

Cost  of  street  paving  in  30  cities  in  Wisconsin  per  sq. 
yd.  (See  Municipal  Journal  and  Engineer,  Nov.,  1905)  as- 
phalt $1.80  to  $2.19;  bricks,  $i  to  $2.19;  macadam  $.25  to 
$1.30;  wood  block  $.60  to  $1.97. 

All-concrete  roadway  paving  has  been  found  in  several 
cities  to  cost  14  to  18  cts.  per  sq.  ft.  At  Jackson,  Mich., 
some  street  paving  having  3  ins.  of  gravel ;  6  ins.  of  i  :8 
cement  and  gravel ;  4  ins.  of  1 13  cement  and  %-in.  crushed 
granite,  mixed  quite  wet,  cost  18  cts.  per  sq.  ft.  (See  Con- 
crete Engineering,  Dec.,  1907,  p.  205.) 

PILES :  Driven  and  cut,  ordinary  lengths  and  sizes, 
spruce  20  to  40  cts.  ft. ;  white  oak,  25  to  60  cts.  ft.  Spruce 
30  to  40  ft.  long,  driven  and  cut,  $6  to  $10  each.  Shorter 
piles  for  trestle  bents  $3  to  $5  in  place. 

PILING:  (Nov.,  1907)  Spruce,  ordinary  cargoes,  6 
to  7  cts.  ft.  Oak,  14-in.  butt,  40  to  50  ft.,  19  cts.  ft. ;  50  to 
55  ft.,  22  cts.  ft;  55  to  60  ft.,  23  cts.  ft.;  60  ft.  and  up,  25 
cts.  ft. 

164 


Pine,  60  to  65  ft.,  $8.50  each;  70  to  75  ft.  $10.50  each; 
80  ft.  and  up,  $16  each. 

Concrete  piles  in  place,  about  $i  per  lineal  foot. 

PIPE:  Vitrified  pipe,  8"  dia.,  15  cts.,  hauling  V*  ct.  ft., 
laying,  ity  cts.  ft.,  cement,  Vz  ct.  ft.  =  17.5  cts.  ft.  in  trench 
already  dug.  For  12"  pipe  the  cost  is  about  35  cts.  per 
ft.  total.  (See  Eng.  Record,  March  10,  1906,  p.  350.) 

RAILING:  Gaspipe,  2-rail,  50  to  75  cts.  ft.,  3-rail,  75 
cts.  to  $1.25  ft. 

A  substantial  bridge  railing  costs  about  $1.50  to  $2.50 
per  lineal  ft.  Cast  iron  newel-posts  about  $10  each. 

ROOFING:  Four  layers  of  felt  paper  covered  with 
pitch  and  gravel  or  pitch  and  slag  4  to  6  cts.  sq.  ft. 

Slate,  7  to  13  cts.  per  sq.  ft.  Slag,  4  cts.  Tin,  8  to  10  cts. 
Shingle,  7  to  10  cts.  per  sq.  ft. 

Tile,  Spanish  $9  to  $12  per  square  of  100  sq.  ft. 

SAND  BLASTING:  (Cleaning)  Large  contracts  i  to 
3  cts.  sq.  ft.  (See  Eng.  News,  Vol.  47,  Page  324.) 

SAND:  Building,  20  to  25  cts.  cu.  yd.  in  bank,  f.  o.  b. 
cars,  40  to  50  cts.  cu.  yd.  freight  for  5o-mile  run,  about 
75  cts.  cu.  yd.,  hauling,  25  to  50  cts.  cu.  yd.  Usual  price 
delivered  about  $1.10  cu.  yd. 

SEEDING:    In  grass  $25  to  $75  acre. 

SEWER  PIPE:  Laying  and  cementing  in  trench  al- 
ready dug,  small  sizes,  15  to  25  cts.  per  ft,  large  sizes  50 
cts.  to  $i  per  ft. 

Cost  of  pipe  per  lineal  ft.,  5",  5  to  7  cts.,  10",  15  to  20  cts. 
15",  25  to  40  cts.,  21",  50  to  75  cts.,  30",  $i  to  $1.70;  48", 

$2  tO  $3. 

SHRUBS :    50  cts.  to  $2  each. 

SODDING:  In  country  towns,  7  to  10  cts.  sq.  yd.,  in 
cities,  25  to  50  cts.  sq.  yd. 

STEEL:  Structural,  material  only,  i%  to  2%  cts.  per 
Ib.  Erected  and  painted,  3  to  5  cts.  per  Ib. 

Castings,  in  place,  5  to  10  cts.  Ib. 

Rails,  new,  $28  ton,  f.  o.  b.  cars;  old,  short  pieces,  $14 
to  $14.50. 

Scrap,  structural,  $14  long  ton. 
165 


STONE:  Wholesale  rates,  delivered  at  N.  Y. ;  price 
per  cu.  ft. 

Nova  Scotia,  in  rough,  90  cts. ;  Ohio  freestone,  in  rough, 
85  to  90  cts. ;  Minnesota  freestone,  in  rough,  90  cts. ;  Long- 
meadow  freestone,  85  cts. ;  Brownstone,  Portland,  ct.,  60 
cts. ;  Brownstone,  Belleville,  N.  J.,  75  cts.  to  $i ;  Scotch 
redstone,  $1.05;  Lake  Superior  redstone,  $1.10;  granite, 
rough,  40  to  50  cts. ;  limestone,  buff  and  blue,  80  cts. ;  por- 
tage, $i ;  Caen,  $1.25  to  $175;  white  building  marble,  $1.25 
to  1.75 ;  Wyoming  bluestone,  90  cts. ;  Euclid  bluestone,  90 
cts. ;  crushed  stone,  $1.40  per  net  ton.  f.  o.  b.  cars  N.  Y. 
C.  (May,  1904.) 

TARRED  PAPER:  i  ply  (roll  300  sq.  ft.),  ton,  $32.50 
to  $35-50;  2  ply,  roll  108  sq.  ft.,  55  to  6oc  roll;  3  ply,  roll 
108  sq.  ft.,  78  to  8oc.  Slater's  Felt  (roll  506  sq.  ft.)  75c. 
R.  R.  M.  Stone  Surfaced  Roofing  (roll  no  sq.  ft.)  $2.75. 

TAR :  Regular  bbl.,  $2.25,  oil  bbl.,  $5.75 ;  Coal  tar,  gal- 
lon, 8  cts. 

TIES,  RAILROAD:  Untreated,  cedar  and  spruce,  40 
to  60  cts.  each ;  oak  and  yellow  pine,  60  to  80  cts.  each. 
See  Trans,  Am.  Ry.  Engineering  and  M.  of  W.  Asso.  Vol. 
2  for  cost  of  ties  to  13  of  the  principal  American  rail- 
roads. It  is  there  shown  to  vary  between  35^  and  Si1/^ 
cents  each. 

TOOLING:  Bush  hammering  concrete  surfaces  2  to  5 
cts.  per  sq.  ft. 

TRANSPORTING:  The  cost  of  picking  up  materials 
such  as  stone  or  sand  and  hauling  them  a  moderate  dis- 
tance in  wheelbarrows  is  about  20  to  25  cts.  per  cu.  yd. 
With  wagons  or  carts  the  cost  is  about  15  to  23  cts.  per 
cu.  yd, 

TREATING  WOOD:  Cheaper  processes  5  to  10  cts. 
per  cu.  ft.  Creosoting  20  to  60  cts.  per  cu.  ft. 

Railroad  ties  20  cts.  each,  up. 

Creosoted  yellow  pine  in  place  costs,  including  cost  of 
wood,  $65  to  $80  per  1,000  ft.  B.  M. 

TREES :    $i  to  $5  each. 

166 


WOOD:  (Prices  per  thousand  feet  of  board  measure) 
May,  1904. 

Hemlock,  rough,  in  lengths  up  to  20  ft.  $17  to  $19. 
Lengths  22  to  40  ft.  $3.25  to  $7  additional. 

Pine,  yellow  (Long  Leaf)  building  orders,  12  ins.  and 
under,  $20.50  to  $22.50;  14-in.  and  up,  $26  to  $29;  1%  and 
iVz-in.  wide  boards,  $28  to  $30;  2-in.  wide  plank,  heart 
face,  $30  to  $31.50. 

Yellow  pine  of  heavy  construction,  in  cargo  lots,  de- 
livered New  York  City,  $22  to  $25. 

Spruce :  random  cargoes,  2-in.  cargoes,  $18  to  $21 ;  6 
to  9-ins.,  cargoes  $19.50  to  $21.50;  10  and  12-in.  cargoes, 
$21  to  $23. 

The  framing  and  placing  of  wood  in  a  structure  costs 
$5  to  $15  per  thousand  feet  of  board  measure. 

White  oak  timber  in  wharf  construction  costs  $50  to 
$60  per  thousand  feet  in  place. 

Bridge  timber  in  place,  per  thousand  feet,  white  oak, 
$40  to  $50 ;  yellow  pine,  $35  to  $45 ;  hemlock,  $22  to  $30. 

More  than  half  the  cost  of  wood  is  generally  due  to 
freight  on  account  of  the  long  distances  between  the  cen- 
ters of  greatest  supply  and  greatest  consumption. 


167 


Specifications  for  Natural  and  Port- 
land Cement.* 

Recommended  Standard  Specifications. 
(Standard  Specifications  for  Cement  adopted  by  a  Joint 
Committee  embracing  representatives  from  the  American 
Society  of  Civil  Engineers,  American  Society  for  Testing 
Materials,    American    Institute   of   Architects,    Engineer 
Department  of  United  States  Army,  Association  of  Port- 
land Cement  Manufacturers  and  American  Railway  En- 
gineering and  Maintenance  of  Way  Association.) 
General  Observations. 

1.  These  remarks  have  been  prepared  with  a  view  of 
pointing  out  the  pertinent  features  of  the  various  require- 
ments and  the  precautions  to  be  observed  in  the  interpreta- 
tion of  the  results  of  the  tests. 

2.  The  Committee  would  suggest  that  the  acceptance  or 
rejection  under  these  specifications  be  based  on  tests  made 
by  an  experienced  person  having  the  proper  means   for 
making  the  tests. 

3.  Specific  gravity  is  useful  in  detecting  adulteration  or 
underburning.     The  results  of  tests  of  specific  gravity  are 
not  necessarily  conclusive  as  an  indication  of  the  quality 
of  a  cement,  but  when  in  combination  with  the  results  of 
other  tests  may  afford  valuable  indications. 

4.  The  sieves  should  be  kept  thoroughly  dry. 

5.  Great  care  should  be  exercised  to  maintain  the  test 
pieces  under  as  uniform  conditions  as  possible.     A  sudden 
change  or  wide  range  of  temperature  in  the  room  in  which 

*  The  specifications  and  recommendations  that  follow 
are  taken  without  change,  except  the  omission  of  figures 
showing  apparatus  and  reference  to  same,  from  Manual  of 
Recommended  Practice,  Edition  of  1907,  published  by 
American  Railway  Engineering  and  Maintenance  of  Way 
Association. 

168 


the  tests  are  made,  a  very  dry  or  humid  atmosphere,  and 
other  irregularities  vitally  affect  the  rate  of  setting. 

6.  Each  consumer  should  fix  the  minimum  requirements 
for  tensile  strength  to  suit  his  own  conditions.    They  shall, 
however,  be  within  the  limits  stated. 

7.  The  tests  for  constancy  of  volume  are  divided  into 
two  classes,  the  first  normal,  the  second  accelerated.     The 
latter  should  be  regarded  as  a  precautionary  test  only,  and 
not  infallible.     So  many  conditions  enter  into  the  making 
and  interpreting  of  it  that  it  should  be  used  with  extreme 
care. 

8.  In  marking  the  pats  the  greatest  care  should  be  ex- 
ercised to  avoid  initial  strains  due  to  molding  or  too  rapid 
drying  out  during  the  first  twenty-four  hours.     The  pats 
should  be  preserved  under  the  most  uniform  conditions  pos- 
sible,   and  rapid  changes  of  temperature  should  be  avoided. 

9.  The  failure  to  meet  the  requirements  of  the  accelerat- 
ed tests  need  not  be  sufficient  cause  for  rejection.    The  ce- 
ment may,  however,  be  held  for  twenty-eight  days,  and  a 
retest  made  at  the  end  of  that  period.    Failure  to  meet  the 
requirements  at  this  time  should  be  considered  sufficient 
cause  for  rejection,  although  in  the  present  state  of  our 
knowledge  it  cannot  be  said  that  such  failure  necessarily 
indicates  unsoundness,  nor  can  the  cement  be  considered 
entirely  satisfactory  simply  because  it  passes  the  tests. 

STANDARD   SPECIFICATIONS   FOR   CEMENT 

GENERAL  CONDITIONS. 
A  11  .     i-    11  u     •  *    j 

1.  All  cement  shall  be  inspected. 

2.  Cement  may  be  inspected  either  at  the  place  of  manu- 
facture or  on  the  work. 

3.  In  order  to  allow  ample  time  for  inspecting  and  test- 
ing, cement   shall  be    stored  in  a    suitable    weather-tight 
building  having  the  floor  properly  blocked  or  raised  from 
the  ground. 

4.  The  cement  shall  be  stored  in  such  a  manner  as  to 
permit  easy  access  for  proper  inspection  and  identification 
of  each  shipment. 

5.  Every  facility  shall  be  provided  by  the  contractor  and 


a  period  of  at  least  twelve  days  allowed  for  the  inspection 
and  necessary  tests. 

6.  Cement  shall  be  delivered  in  suitable  packages  with 
the  brand  and  name  of  manufacturer  plainly  marked  there- 
on. 

7.  A  bag  of  cement  shall  contain  94  pounds  of  cement 
net.     Each  barrel  of  Portland  cement  shall  contain   four 
bags,  and  each  barrel  of  Natural  cement  shall  contain  three 
bags  of  the  above  net  weight. 

8.  Cement  failing  to  meet  the  seven-day  requirements 
may  be  held  awaiting  the  results  of  the  twenty-eight  day 
tests  before  rejection. 

9.  All  tests  shall  be  made  in  accordance  with  the  meth- 
ods proposed  by  the  Committee  on  Uniform  Tests  of  Ce- 
ment of  the  American  Society  of  Civil  Engineers,  presented 
to  the  Society  January  21,  1903,  and  amended  January  20, 
1904,  with  all  subsequent  amendments  thereto  (See  adden- 
dum to  these  specifications.) 

10.  The  acceptance  or  rejection  shall  be  based  on  the 
following  requirements : 

NATURAL  CEMENT. 

IT.  This  term  shall  be  applied  to  the  finely  pulverized 
product  resulting  from  the  calcination  of  an  argillaceous 
limestone  at  a  temperature  only  sufficient  to  drive  off  the 
carbonic  acid  gas. 

12.  The  specific  gravity  of  the  cement,  thoroughly  dried 
at  100°  C,  shall  not  be  less  than  2.8. 

13.  It  shall  leave  by  weight  a  residue  of  not  more  than  10 
per  cent,  on  the  No.  100,  and  30  per  cent,  on  the  No.  200 
sieve. 

14.  It  shall  develop  initial  set  in  not  less  than  ten  min- 
utes, and  hard  set  in  not  less  than  thirty  minutes,  nor  more 
than  three  hours. 

15.  The  minimum  requirements  for  tensile  strength  for 
briquettes  one  inch  square  in  cross-section  shall  be  within 

170 


the   following  limits,   and  shall   show  no  retrogression  in 
strength  within  the  periods  specified:* 
Age.                            Neat  Cement.  Strength 

24  hours  in  moist  air 50-100  Ibs. 

7  days  (i  day  in  moist  air,  6  days  in  water)  .  .100-200  Ibs. 

28  days  (i  day  in  moist  air,  27  days  in  water)    200-300  Ibs. 

One  Part  Cement,  three  Parts  Standard  Sand. 

7  days  (i  day  in  moist  air,    6  days  in  water)     25-  75  Ibs. 
28  days  (i  day  in  moist  air,  27  days  in  water)     75-100  Ibs. 

16.  Pats  of  neat  cement  about  three  (3)  in.  in  diameter, 
one-half  (Vz)  in.  thick  at  center,  tapering  to  a  thin  edge, 
shall  be  kept  in  moist  air  for  a  period  of  twenty-  four  hours. 

(a)  A  pat  is  then  kept  in  air  of  normal  temperature. 

(b)  Another  is  kept  in  water  maintained  as  near  70° 
F.  as  practicable. 

17.  These  pats  are  observed  at  intervals  for  at  least  28 
days,  and,  to  satisfactorily  pass  the  tests,   should   remain 
firm  and  hard  and  show  no  signs  of  distortion,  checking, 
cracking  or  disintegrating. 

PORTLAND    CEMENT. 

18.  This  term  shall  be  applied  to  the  finely  pulverized 
product  resulting  from  the  calcination  to  incipient  fusion 
of  an  intimate  mixture   of  properly  proportioned  argilla- 
ceous and  calcareous  materials,  and  to  which  no  addition 
greater  than  3  per  cent,  has  been  made  subsequent  to  calci- 
nation. , 

19.  The  specific  gravity  of  the  cement,  thoroughly  dried 
at  100°  C,  shall  be  not  less  than  3.10. 

20.  It  shall  leave  by  weight  a  residue  of  not  more  than 
8  per  cent,  on  the  No.  100,  and  not  more  than  25  per  cent, 
on  the  No.  200  sieve. 

21.  It  shall  develop  initial  set  in  not  less  than  thirty 


*  For  example,  the  minimum  requirement  for  the  twen- 
ty-four hour  neat  cement  tests  should  show  some  specified 
value  within  the  limits  of  50  and  100  pounds,  and  so  on  for 
each  period  stated. 

171 


minutes,  but  must  develop  hard  set  in  not  less  than  one 
hour,  nor  more  than  ten  hours. 

22.  The  minimum  requirements  for  tensile  strength  for 
briquettes  one-inch  square  in  cross-section  shall  be  within 
the   following  limits,   and  shall   show  no   retrogression  in 
strength  within  the  periods  specified.* 

Age.  Neat  Cement.  Strength. 

24  hours  in  moist  air  150-200  Ibs. 

7  days  (i  day  in  moist  air,    6  days  in  water)     450-55°  Ibs. 

28  days  (i  day  in  moist  air,  27  days  in  water)     550-650  Ibs. 

One  Part  Cement,  Three  Parts  Standard  Sand. 

7  days  (i  day  in  moist  air,  6  days  in  water)  150-200  Ibs. 
28  days  (i  day  in  moist  air,  27  days  in  water)  200-300  Ibs. 

23.  Pats  of  neat  cement  about  three  (3)  in.  in  diameter, 
one-half  (%)  in.  thick  at  the  center,  and  tapering  to  a  thin 
edge,  shall  be  kept  in  moist  air  for  a  period  of  twenty-four 
hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature  and 
observed  at  intervals  for  at  least  28  days. 

(b)  Another  pat  is  kept  in  water  maintained  as  near 
70°  F.  as  practicable,  and  observed  at  intervals  for  at  least 
28  days,     :9toa?  tsJ  •* 

(c)  A  third  pat  is  exposed  in  any  convenient  way  in  an 
atmosphere  of    steam,  above    boiling    water,  in  a    loosely 
closed  vessel  for  five  hours. 

24.  These  pats,  to  satisfactorily  pass  the  requirements, 
shall  remain  firm  and  hard  and  show  no  signs  of  distortion, 
checking,  cracking  or  disintegrating. 

25.  The  cement  shall  not  contain  more  than   1.75  per 
cent,  of  anhydrous  sulphuric  acid  (SO3),  nor  more  than  4 
per  cent,  of  magnesia  (MgO). 


*  For  example,  the  minimum  requirement  for  the  twen- 
ty-four hour  neat  cement  tests  should  show  some  specified 
value  within  the  limits  of  150  and  200  pounds,  and  so  on 
for  each  period  stated. 

172 


ADDENDUM. 

ABSTRACT   OF    METHODS    RECOMMENDED   BY   THE    SPECIAL   COM- 
MITTEE ON   UNIFORM   TESTS   OF  CEMENT  OF  THE   AMERI-    .  . 
CAN   SOCIETY  OF  CIVIL  ENGINEERS. 
SAMPLING. 

1.  The  sample  shall  be  a  fair  average  of  the  contents  of 
the  package;  it  is  recommended  that,  where  conditions  per- 
mit, one  barrel  in  every  ten  be  sampled. 

2.  All  samples  should  be  passed  through  a  sieve  having 
twenty  meshes  per  linear  inch,  in  order  to  break  up  lumps 
and  remove  foreign  material ;  this  is  also  a  very  effective 
method  for  mixing  them  together  in  order  to  obtain  an 
average.    For  determining  the  characteristics  of  a  shipment 
of  cement,  the  individual  samples  may  be  mixed  and  the 
average  tested;  where  time  will  permit,  however,  it  is  rec- 
ommended that  they  be  tested  separately. 

3.  Cement  in  barrels  should  be  sampled  through  a  hole 
made  in  the  center  of  one  of  the  staves,  midway  between 
the  heads,  or  in  the  head,  by  means  of  an  auger  or  a  samp- 
ling iron  similar  to  that  used  by  sugar  inspectors.     If  in 
bags,  it  should  be  taken  from  surface  to  center. 

CHEMICAL  ANALYSIS. 

4.  As  a  method  to  be  followed  for  the  analysis  of  ce- 
ment, that  proposed  by  the  Committee  on  Uniformity  in 
the  Analysis  of  Materials  for  the  Portland  Cement  Indus- 
try, of  the  New  York  Section  of  the  Society  for  Chemical 
Industry,  and  published  in  the  Journal  of  the  Society  for 
January  15,  1902,  is  recommended. 

SPECIFIC  GRAVITY. 

5.  The  determination  of  specific  gravity  is  most  conven- 
iently made  with  Le  Chatelier's  apparatus.    This  consists  of 
a  flask  of  120  cu.  cm.   (7.32  cu.  in.)  capacity,  the  neck  of 
which  is  about  20  cm.  (7.87  in.)  long;  in  the  middle  of  this 
neck  is  a  bulb,  above  and  below  which  are  two  marks ;  the 
volume  between  these  marks  is  20  cu.  cm.   (1.22  cu.  in.) 
The  neck  has  a  diameter  of  about  9  mm.  (0.35  in.),  and  is 
graduated  into  tenths  of  cubic  centimeters  above  the  mark. 

173 


6.  Benzine  (62°  Baume  naptha),  or  kerosene  free  from 
water,  should  be  used  in  making  the  determination. 

7.  The  specific  gravity  can  be  determined  in  two  ways : 
(a)     The  flask  is  filled  with  either  of  these  liquids  to 

the  lower  mark  and  64  gr.  (2.25  oz.)  of  powder,  previously 
dried  at  100°  C  (212°  F.)  and  cooled  to  the  temperature 
of  the  liquid,  is  gradually  introduced  through  the  funnel 
[the  stem  of  which  extends  into  the  flask  to  the  top  of  the 
bulb],  until  the  upper  mark  is  reached.  The  difference  in 
weight  between  the  cement  remaining  and  the  original  quan- 
tity (64  gr.)  is  the  weight  which  has  displaced  20  cu.  cm. 

8.  (b)     The  whole  quantity  of  the  powder  is  introduced, 
and  the  level  of  the  liquid  rises  to  some  division  of  the  grad- 
uated neck.     This  reading  plus  20  cu.  cm.  is  the  volume 
displaced  by  64  gr.  of  the  powder. 

9.  The  specific  gravity  is  then  obtained  from  the  for- 
mula: 

Weight  of  Cement 

Specific  Gravity  = 

Displaced  Volume 

10.  The  flask,  during  the  operation,  is  kept  immersed  in 
water  in  a  jar,  in  order  to  avoid  variations  in  the  tempera- 
ture of  the  liquid.    The  results  should  agree  within  o.oi. 

11.  A  convenient  method  for  cleaning  the  apparatus  is 
as  follows:  The  flask  is  inverted  over  a  large  vessel,  pre- 
ferably a  glass  jar,  and  shaken  vertically  until  the  liquid 
starts  to  flow  freely;  it  is  then  held  still  in  a  vertical  posi- 
tion until  empty ;  the  remaining  traces  of  cement  can  be  re- 
moved in  a  similar  manner  by  pouring  into  the  flask  a  small 
quantity  of  clean  liquid  and  repeating  the  operation. 

FINENESS. 

12.  The  sieves  should  be  circular,  about  20  cm.  (7.87  in.) 
in  diameter,  6  cm.    (2.36  in.)    high,  and    provided    with  a 
pan  5  cm.     (1.97  in.)  deep,  and  a  cover. 

13.  The  wire  cloth  should  be  woven  (not  twilled)  from 
brass  wire  having  the  following  diameters : 

No.  100,  0.0045  in. ;  No.  200,  0.0024  in. 

14.  This  cloth  should  be  mounted  on  the  frames  without 

174 


distortion;  the  mesh  should  be  regular  in  spacing  and  be 
within  the  following  limits : 

No.  TOO,    96  to  100  meshes  to  the  linear  inch. 

No.  200,  188  to  200  meshes  to  the  linear  inch. 

15.  Fifty  grams  (1.76  oz.)  or  100  gr.  (3.52  oz.)  should  be 
used  for  the  test,  and  dried  at  a  temperature  of  100°  C. 
(2i2°F.)  prior  to  sieving. 

16.  The  thoroughly  dried  and  coarsely  screened  sample 
is  weighed  and  placed  on  the  No.  200  sieve,  which,  with 
pan  and  cover  attached,  is  held  in  one  hand  in  a  slightly  in- 
clined position,  and  moved  forward  and  backward,  at  the 
same  time  striking  the  side  gently  with  the  palm  of  the 
other  hand,  at  the  rate  of  about  200  strokes  per  minute. 
The  operation  is  continued  until  not  more  than  one-tenth 
of  I  per  cent,  passes  through  after  one  minute  of  continu- 
ous sieving.     The  residue  is  weighed,  then  placed  on  the 
No.  loo  sieve  and  the  operation  repeated.     The  work  may 
be  expedited  by  placing  in  the  sieve  a  small  quantity  of 
large  shot.    The  results  should  be  reported  to  the  nearest 

tenth  of  i  per  cent. 
r 

NORMAL  CONSISTENCY. 

17.  This    best  can  be    determined  by    means    of.  Vicat 
Needle  Apparatus,  which  consists  of  a  frame,  bearing  a 
movable  rod  with  a  cap  at  one  end,  and  at  the  other  a  cyl- 
inder, i  cm.  (0.39  in.)  in  diameter,  the  cap,  rod  and  cylin- 
der weighing  300  gr.   (10.58  oz.).     The  rod,  which  can  be 
held  in  any  desired  position  by  a  screw,  carries  an  indica- 
tor, which  moves  over  a  scale  (graduated  to  centimeters) 
attached  to  the  frame.    The  paste  is  held  by  a  conical  hard- 
rubber  ring,  7  cm.    (2.76  in.)    in  diameter  at  the  base;  4 
cm.  (1.57  in.)  high,  resting  on  a  glass  plate  about  10  cm. 
(3.94  in.)  square. 

18.  In  making  the  determination,  the  same  quantity  of 
cement  as  will  be  subsequently  used  for  each  batch  in  mak- 
ing the  briquettes  [but  not  less  than  500  gr.   (17.16  oz.)] 
is  kneaded  into  a  paste,  as  described  in  paragraph  38,  and 
quickly  formed  into  a  ball  with  the  hands,  completing  the 
operation  by   tossing  it  six    times  from  one    hand  to   the 

175 


other,  maintained  6  in.  apart;  the  ball  is  then  pressed  into 
the  rubber  ring,  through  the  larger  opening,  smoothed  off 
and  placed  (on  its  large  end)  on  a  glass  plate  and  the 
smaller  end  smoothed  off  with  a  trowel ;  the  paste,  confined 
in  the  ring,  resting  on  the  plate,  is  placed  under  the  rod 
bearing  the  cylinder,  which  is  brought  in  contact  with  the 
surface  and  quickly  released. 

19.  The  paste  is  of  normal  consistency  when  the  cyl- 
inder penetrates  to  a  point  in  the  mass  10  mm.   (0.39  in.) 
below  the  top  of  the  ring.    Great  care  must  be  taken  to  fill 
the  ring  exactly  to  the  top. 

20.  The  trial  pastes  are  made  with  varying  percentages 
of  water  until  the  correct  consistency  is  obtained. 

Note.  The  Committee  of  Standard  Specifications  for 
Cement  inserts  the  following  table  for  temporary  use,  to 
be  replaced  by  one  to  be  devised  by  the  Committee  of  the 
American  Society  of  Civil  Engineers. 

PERCENTAGE  OF  WATER  FOR  STANDARD  MIXTURES. 


Neat  II.  I  I 

1.  211.3 

1  .4  1  1  .5||Neat  1  1  _  1  1  1  .2  1  1  .3  !  1  .4  1  1  .5, 

18 
19 

12.0 
12.3 

10.0 
10.2 

9.0 
9.2 

8.4 
8.5 

8.0] 
8.1 

|   33 
34 

17.0 
17.3 

13.311  I.5|I0.4 
13.6  11.7)10.5 

9.6 
9.7 

20 

12.7 

10.4 

9.3 

8.7 

8.2J 

35 

17.7 

13.8  1  1.8 

10.7 

9.9 

21 

13.0 

10.7 

9.5 

8.8 

8.3 

36       18.0 

14.0)12.0 

10.8 

10.0 

22 

13.3 

10.9 

9.7 

8.9 

8.4 

37      118.3 

14.2  12.2 

109 

10.  1 

23 

13.7 

1  I.I 

9.8 

9.1 

8.5 

38      |I8.7 

14.4 

12.3 

1  I.I 

10.2 

24 

14.0 

1  1.3 

10.0 

9.21   8.6 

39      1  19.0 

14.7 

12.5 

11.2 

10.3 

25 

14.3 

11.6 

10.2 

9.3J   8.8 

40 

19.3 

14.9 

I2.7H  1.3 

10.4 

26 

14.7 

11.8 

10.3 

9.5!   8.9 

41 

19.7 

15.1 

12.8)11.5 

10.5 

27 

15.0 

12.0 

10.5 

9.6|    9.0 

|  42      |20.0  15.3 

13.0)11.6 

10.6 

28 

I5.3|  12.2 

10.7 

9.7|   9.1 

1   43 

20.3115.6 

13.2 

1  1.7 

10.7 

29 

I5.7JI2.5 

10.8 

9.9 

9.2 

|  44 

20.7115.8 

13.3 

11.9 

10.8 

30 

16.0  12.7 

1  1.0 

10.0 

9.3 

|   45 

21.0(16.0 

I3.5|  12.0 

1  1.0 

31 

16.3112.9 

11.2 

10.1 

9.4 

46 

21.3  16.  1 

13.7112.1 

II.  1 

32 

16.7)13.1 

1  1.3)10.3 

9.5 

! 

...  |... 

__.|_ 

to    I  !  I    to  2  |  I    to  3  |  I    to  4  I  I    to  5 


Cement   

500 

333 

250 

|  200 

167 

Sand  

500 

667 

750 

)  800 

833 

TIME  OF  SETTING. 

21.  For  this  purpose  the  Vicat  Needle,  which  has  al- 
ready been  described  in  paragraph  17,  should  be  used. 

22.  In  making  the  test,  a  paste  of  normal  consistency 
is  molded  and  placed  under  the  rod,  as  described  in  para- 

176 


graph  18 ;  this  rod,  bearing  the  cap  at  one  end  and  the  nee- 
dle, I  mm.  (0.039  in.)  in  diameter,  at  the  other,  weighing 
300  gr.  (10.58  oz.).  The  needle  is  then  carefully  brought  in 
contact  with  the  surface  of  the  paste  and  quickly  released. 

23.  The  setting  is   said  to  have  commenced  when  the 
needle  ceases  to  pass  a  point  5  mm.   (0.20  in.)   above  the 
upper  surface  of  the  glass  plate,  and  is  said  to  have  termi- 
nated the  moment  the  needle  does  not  sink  visibly  into  the 
mass. 

24.  The  test  pieces  should  be  stored  in  moist  air  during 
the  test;  this  is  accomplished  by  placing  them  on  a  rack 
over  water  contained  in  a  pan  and  covered  with  a  damp 
cloth,  the  cloth  to  be  kept  away  from  them  by  means  of  a 
wire  screen ;  or  they  may  be  stored  in  a  moist  box  or  clos- 
et. 

25.  Care  should  be  taken  to  keep  the  needle  clean,  as 
the  collection  of  cement  on  the  sides  of  the  needle  retards 
the  penetration,  while  cement  on  the  point  reduces  the  area 
and  tends  to  increase  the  penetration. 

26.  The  determination  of  the  time  of  setting  is  only  ap- 
proximate, being  materially  affected  by  the  temperature  of 
the  mixing  water,  the  temperature  and  humidity  of  the  air 
during  the    test,  the    percentage  of  water    used,  and    the 
amount  of  molding  the  paste  receives. 

STANDARD  SAND. 

27.  For  the    present,  the    Committee    recommends    the 
natural  sand  from  Ottawa,  111.,  screened  to  pass  a  sieve 
having  20  meshes  per  linear  inch  and  retained  on  a  sieve 
having  30  meshes  per  linear  inch;  the  wires  to  have  diam- 
eters of  0.0165  and  0.0112  in.,  respectively,  *.  e,,  half  the 
width  of  the  opening  in  each  case.    Sand  having  passed  the 
No.  20  sieve  shall  be  considered  standard  when  not  more 
than  i  per  cent,  passes  a  No.  30  sieve  after  one  minute  con- 
tinuous sifting  of  a  50o-gr.  sample. 

28.  The  Sandusky  Portland  Cement  Company  of  San- 
dusky,  Ohio,  has  agreed  to  undertake  the  preparation  of 
this  sand  and  to  furnish  it  at  a  price  only  sufficient  to  cover 
the  actual  cost  of  preparation. 

177 


FORM   OF  BRIQUETTE. 

29.  While  the  form  of  the  briquette  recommended  by  a 
former  Committee  of  the  Society  is  not  wholly  satisfactory, 
this  Committee  is    not  prepared  to    suggest    any    change, 
other  than  rounding  off  the  corners  by  curves  of  %-in. 
radius. 

MOLDS. 

30.  The  molds  should  be  made  of  brass,  bronze  or  some 
equally  non-corrodible  material,  having  sufficient  metal  in 
the  sides  to  prevent  spreading  during  molding. 

31.  Gang  molds,   which   permit   molding   a   number   of 
briquettes  at  one    time,    are  preferred  by    many  to    single 
molds;  since  the  greater  quantity  of  mortar  than  can  be 
mixed  tends  to  produce  a  greater  uniformity  in  the  results. 

32.  The  molds  should  be  wiped  with  an  oily  cloth  be- 
fore using. 

MIXING. 

33.  All  proportion  should  be  stated  by  weight ;  the  quan- 
tity of  water  to  be  used  should  be  stated  as  a  percentage 
of  the  dry  material. 

34.  The  metric  system  is  recommended  because  of  the 
convenient  relation  of  the  gram    and  the  cubic  centimeter. 

35.  The  temperature  of  the  room  and  the  mixing  water 
should  be  as  near  21°  C.   (70°  F.)  as  it  is  practicable  to 
maintain  it. 

36.  The  sand  and  cement  should  be  thoroughly  mixed 
dry.     The  mixing  should  be  done  on  some  non-absorbing 
surface,   preferably   plate   glass.     If  the   mixing   must   be 
done  on  an    absorbing    surface  is    should  be    thoroughly 
dampened  prior  to  use. 

37.  The  quantity  of  material  to  be  mixed  at  one  time 
depends  on  the  number  of  test  pieces  to  be  made;  about 
1,000  gr.  (35.28  oz.)   makes  a  convenient  quantity  to  mix, 
especially  by  hand  methods. 

38.  The  material  is  weighed  and  placed  on  the  mixing 
table,  and  a  crater  formed  in  the  center,  into  which  the 
proper  percentage  of  clean  water  is  poured;  the  material 
on  the  outer  edge  is  turned  into  the  crater  by  the  aid  of  a 

178 


trowel.  As  soon  as  the  water  has  been  absorbed,  which 
should  not  require  more  than  one  minute,  the  operation  is 
completed  by  vigorously  kneading  with  the  hands  for  an 
additional  iMj  minutes,  the  process  being  similar  to  that 
used  in  kneading  dough.  A  sandglass  affords  a  convenient 
guide  for  the  time  of  kneading.  During  the  operation  of 
mixing  the  hands  should  be  protected  by  gloves,  preferably 
of  rubber. 

MOLDING. 

39.  Having  worked  the  paste  or  mortar  to  the  proper 
consistency,  it  is  at  once  placed  in  the  molds  by  hand. 

40.  The  molds    should  be    filled  at   once,  the    material 
pressed  in  firmly  with  the  fingers  and  smoothed  off  with 
a  trowel  without  ramming;  the  material  should  be  heaped 
up  on  the  upper  surface  of  the  mold,  and,  in  smoothing  off, 
the  trowel  should  be  drawn  over  the  mold  in  such  a  man- 
ner as  to  exert  a  moderate  pressure  on  the  excess  material. 
The  mold  should  be  turned  over  and  the  operation  repeated. 

41.  A  check    upon  the    uniformity  of    the  mixing    and 
molding  is  afforded  by  weighing  the  briquettes  just  prior 
to    immersion,  or  upon    removal   from  the    moist    closet. 
Briquettes  which  vary  in  weight  more  than  3  per  cent,  from 
the  average  should  not  be  tested. 

STORAGE  OF  THE  TEST  PIECES. 

42.  During  the    first  24  hours  ^fter    molding,    the  test 
pieces  should  be  kept  in  moist  air  to  prevent  them  from 
drying  out. 

43.  A  moist  closet  or  chamber  is  so  easily  devised  that 
the  use  of  the  damp  cloth  should  be  abandoned  if  possible. 
Covering  the  test  pieces  with  a  damp  cloth  is  objectionable, 
as  commonly  used,  because  the  cloth  may  dry  out  unequal- 
ly, and  in  consequence  the  test  pieces  are  not  all  maintained 
under  the  same  condition.     Where  a  moist  closet  is  not 
available,  a  cloth  may  be  used  and  kept  uniformly  wet  by 
immersing  the  ends  in  water.     It  should  be  kept  from  di- 
rect contact  with  the  test  pieces  by  means  of  a  wire  screen 
or  some  similar  arrangement. 

44.  A  moist  closet  consists  of  a  soapstone  or  slate  box, 

179 


or  a  metal-lined  wooden  box — the  metal  lining  being  cov- 
ered with  felt  and  this  felt  kept  wet.  The  bottom  of  the 
box  is  so  constructed  as  to  hold  water,  and  the  sides  are 
provided  with  cleats  for  holding  glass  shelves  on  which  to 
place  the  briquettes.  Care  should  bye  taken  to  keep  the  air 
in  the  closet  uniformly  moist. 

45.  After  24  hours  in  moist  air,  the  test  pieces  for  lon- 
ger periods  of  time  should  be  immersed  in  water  main- 
tained as  near  21°  C.  (70°  F.)  as  practicable;  they  may  be 
stored  in  tanks  or  pans,  which  should  be  of  non-corrodible 
material. 

TENSILE    STRENGTH. 

46.  The  tests  may  be  made  on  any  standard  machine.    A 
solid  metal  clip  is  recommended.     This  clip  is  to  be  used 
without  cushioning  at  the  points  of  contact  with  the  test 
specimen.     The  bearing  at  each  point  of  contact  should  be 
^4-in.  wide,  and  the  distance  between  the  centers  of  contact 
on  the  same  clip  should  be  I1A  in. 

47.  Test  pieces  should  be  broken  as  soon  as  they  are 
removed  from  the  water.    Care  should  be  observed  in  cen- 
tering the  briquettes  in  the  testing  machine,  as  cross-strains, 
produced  by  improper  centering,  tend  to  lower  the  break- 
ing strength.    The  load  should  not  be  applied  too  suddenly, 
as  it  may  produce  vibration,  the  shock  from  which  often 
breaks  the  briquette  before  the  ultimate  strength  is  reached. 
Care  must  be  taken  that  the  clips  and  the  sides  of  the  bri- 
quette be  clean  and  free  from  grains  of  sand  or  dirt  which 
would  prevent  a  good  bearing.    The  load  should  be  applied 
at  the  rate  of  600  Ibs.  per  minute.    The  average  of  the  bri- 
quettes of  each  sample  tested  should  be  taken  as  the  test 
excluding  any  results  which  are  manifestly  faulty. 

CONSTANCY   OF  VOLUME. 

48.  Tests  for  constancy  of  volume  are  divided  into  two 
classes:   (i)   Normal  tests,  or  those  made  in  either  air  or 
water  maintained  at  about  21°  C.   (70°  F.),  and   (2)   ac- 
celerated tests,  or  those  made  in  air,  steam  or  water  at  a 
temperature     of  45°  C.   (115°  F.)   and  upward.     The  test 
pieces  should  be  allowed  to  remain  24  hours  in  moist  air 

180 


before   immersion   in   water  or   steam,   or  preservation  in 
air. 

49.  For  these  tests,  pats  about  7%  cm.   (2.95  in.)  in  di- 
ameter, i}4  cm.  (0.49  in.)  thick  at  the  center,  and  tapering 
to  a  thin  edge,  should  be  made,  upon  a  clean  glass  plate 
[about  10  cm.  (3.94  in.)  square],  from  cement  paste  of  nor- 
mal consistency. 

50.  A  pat  is  immersed  in  water  maintained  as  near  21° 
C.  (70°  F.)  as  possible  for  28  days,  and  observed  at  inter- 
vals.    A  similar  pat  is  maintained  in  air  at  ordinary  tem- 
perature and  observed  at  intervals. 

51.  A  pat  is  exposed  in  any  convenient  way  in  an  atmos- 
phere of  steam,  above  boiling  water,  in  a  loosely  closed 
vessel. 

52.  To   pass   these   tests   satisfactorily,   the   pats   should 
remain  firm  and  hard,  and  show  no  signs  of  cracking,  dis- 
tortion or  disintegration. 

53.  Should  the  pat  leave  the  plate,  distortion  may  be  de- 
tected best    with    a    straight-edge    applied  to  the    surface 
which  was  in  contact  with  the  plate. 


181 


The  Design  of  Concrete-Steel 
Beams  and  Slabs. 

The  formulas  for  proportioning  concrete-steel  beams  are 
legion,  and  they  are  far  more  varied  than  those  for  the 
design  of  columns  with  which  engineering  literature  was 
flooded  a  decade  or  two  ago.  Nice  formulas  for  the  design 
of  columns  were  elaborated  in  the  days  before  tests  were 
so  common  that  were  satisfactory  in  every  respect,  except 
that  they  did  not  agree  with  the  results  of  tests  that  were 
subsequently  made.  Investigators  later  found  that  the 
behavior  of  compression  members  of  practical  proportions 
agreed  very  closely  with  a  simple  little  straight  line 
formula.  Even  at  the  present  time  the  last  of  these  com- 
plex formulas  has  not  been  weeded  out  of  specifications. 

Another  feature  of  construction  that  has  yielded  to  the 
simplifying  influence  of  development,  or  the  developing 
influence  of  simplification,  relates  to  the  ultimate  and  the 
working  stress  of  steel.  The  two  grades  of  structural 
steel,  with  separate  unit  stresses,  though  they  are  still 
recognized  in  some  specifications,  are  gradually  merging 
into  one  grade  for  all  pieces  subject  to  the  ordinary  pro- 
cesses of  the  shop,  excepting  forging  ;  and  the  manufacturer 
no  longer  needs  to  exhibit  his  ability  to  bring  forth  either 
grade  from  the  same  melt,  bloom,  billet  or  finished  piece. 

Concrete-  steel  designing  is  young,  and  probably  on  ac- 
count of  its  rapid  growth  the  infant  is  afflicted  with  both 
of  the  above-named  ailments.  The  formulas  brought  out 
rival  those  for  retaining  walls  in  complexity,  and  the  units 
recommended  are  about  as  numerous  as  the  formulas. 

The  foregoing  may  seem  an  inconsistent  preface  to  a 
paper  suggesting  both  formulas  and  unit  stresses,  but  the 
writer's  purpose  is  to  show  the  busy  engineer,  who  does 
not  want  to  delve  into  abstruse  mathematics,  that  formulas 
for  the  design  of  concrete-steel  beams  or  slabs  can  be 
made  as  simple  as  those  for  steel  beams.  In  fact,  the 
formulas  are  even  more  simple  than  formulas  for  steel 


in  bending,  if  certain  rules  of  proportioning  be  adopted. 
Further,  the  agreement  between  the  formulas  and  the 
actual  strength  of  the  construction  is  about  as  close  as  in 
steel  construction,  as  many  tests  closely  approximating 
the  proportions  here  recommended  have  demonstrated. 

In  the  matter  of  variation  from  an  established  unit 
stress  we  commonly  allow  steel  to  vary  about  8  per  cent 
either  way  from  a  desired  average  tensile  strength.  We 
should  be  satisfied  if  concrete-steel  tests  show  as  close 
agreement  with  their  calculated  strength,  especially  as 
the  variation,  barring  the  effects  of  careless  work,  will 
probably  be  on  the  safe  side  in  nearly  every  case.  The 
last-named  condition  obtains  because  of  the  real  but  un- 
certain element  of  strength  imparted  to  the  combination 
of  concrete  and  steel  by  the  strength  possessed  by  the  steel 
after  it  has  passed  its  elastic  limit,  the  nominal  limit  of 
ultimate  strength. 

There  are  many  kinds  of  concrete,  just  as  there  are  many 
grades  of  oak.  Some  oak  has  knots  and  wind  shakes  and 
is  unfit  for  use  in  a  structure,  but  specifications  for  oak 
beams  do  not  recognize  these  grades  in  allowing  unit 
stresses ;  rather  the  aim  is  to  exclude  those  grades  unfit 
for  use  by  proper  selection  and  inspection  of  the  materials. 
So  in  concrete-steel  construction  there  should  be  a  standard, 
and  this  should  be  a  concrete  suitable  for  the  purpose  and 
made  strictly  according  to  the  requirements,  as  near  as 
these  ends  can  be  accomplished  commercially. 

It  is  almost  universally  agreed  that  concrete  composed 
of  I  part  Portland  cement,  2  parts  sand  and  4  parts  small 
hard  broken  stone  or  gravel,  or  of  proportions  closely 
approximating  these,  is  the  most  suitable  mixture  for  the 
concrete.  For  cinder  concrete  the  same  proportions,  using 
cinders  in  place  of  broken  stone,  may  be  called  standard. 
It  is  also  common  knowledge  that  this  stone  concrete, 
when  made  of  good  materials,  will  sustain  an  ultimate 
crushing  load  of  about  2,000  Ibs.  per  in.,  and  the  cinder 
concrete  will  take  about  750  Ibs.  per  sq.  in.  It  is  pre- 
183 


sumed^in  all  cases  that  the  materials  and  workmanship 
are  good,  just  as  we  presume  that  wood  used  in  structures 
is  good  and  sound. 

It  is  further  almost  generally  agreed  that  the  ultimate 
strength  of  a  concrete-steel  beam  is  reached  when  the 
steel  is  strained  to  its  elastic  limit  and  the  concrete  has 
reached  its  ultimate  strength. 

The  use  of  steel  having  high  elastic  limit  and  depend- 
ence upon  high  safe  units  in  consequence  is  indefensible. 
The  excessive  stretch  in  the  steel  will  crack  the  concrete. 
The  writer  made  a  number  of  tests  on  the  floors  of  a  large 
concrete-steel  building,  and  in  one  case,  in  a  bay  con- 
taining 13  beams,  91  cracks  were  counted  in  the  beams  when 
the  "safe"  load  was  placed  upon  the  floor.  One  beam  had 
16  cracks.  Many  of  these  appeared  long  before  the  sup- 
posed safe  load  was  placed.  The  deflection  was  excessive. 
This  building  was  designed  with  steel  of  high  elastic  limit, 
and  dependence  was  placed  upon  the  high  tensile  value 
of  the  steel  to  sustain  the  loads. 

The  theoretic  elongation  of  the  concrete,  even  at  mod- 
erate tensile  values  in  the  steel,  corresponds  to  excessive 
tensile  values  in  the  concrete;  and  the  fact  that  concrete 
in  which  steel  is  embedded  has  been  stretched  out  in 
tests  without  cracking  to  elongations  that  would  rupture 
plain  concrete  is  evidence  that  the  concrete  in  setting  has 
shrunk,  thus  putting  the  steel  under  an  initial  compression, 
which  must  be  overcome  before  any  stretch  occurs  in 
the  concrete.  This  shrinking  of  concrete  in  setting  is  one 
of  its  most  useful  properties,  viewed  as  a  medium  in  con- 
crete-steel construction.  Besides  giving  the  embedded 
steel  an  initial  compression  and  thus  helping  its  tensile 
value,  it  also  grips  the  steel,  and  thus  takes  firm  hold  upon 
it,  greatly  aiding  the  adhesion  of  the  concrete  to  the  steel. 
It  is  to  be  noted  that  this  gripping  of  the  steel,  and  not 
mere  adhesion  due  to  contact,  is  the  thing  that  makes 
the  union  between  the  steel  and  the  concrete  effective. 
This  is  the  reason  why  round  and  square  bars  hold  better 
184 


in  the  concrete  than  flats.  It  is  also  a  reason  for  bed- 
ding the  steel  deep  enough  from  the  surface  of  the  con- 
crete to  make  the  gripping  effective.  It  further  overcomes 
the  almost  infinitesimal  reduction  in  diameter  in  the  em- 
bedded steel  when  under  stress  below  the  elastic  limit,  so 
that  the  adhesion  or  skin  friction  is  not  lost  when  the  steel 
elongates  slightly. 

The  fact  that  concrete  shrinks  in  setting  further  points 
out  the  error  in  depending  for  compression  upon  steel 
embedded  in  concrete,  unless  the  concrete  is  merely  used 
for  its  protecting  value.  The  initial  compression  in  the 
steel  adds  an  uncertain  amount  to  any  calculated  compres- 
sion in  the  same.  Steel  reinforcement  in  the  intrados  of 
segmental  concrete  floor  arches  is  not  rational  design,  as 
the  steel,  to  be  useful,  must  be  in  compression.  Steel 
embedded  in  concrete  columns  as  hoops  or  spirals  is 
rational,  as  loading  the  column  tends  to  increase  its 
diameter  and  to  put  tensile  stress  in  the  steel.  Also  light 
longitudinal  rods,  wired  to  these  spirals  to  take  flexure 
in  the  columns,  is  excellent  to  reinforce  the  column  against 
eccentric  or  lateral  forces. 

Another  phase  of  this  shrinking  is  that  very  long  units 
in  concrete-steel  construction  should  not  be  placed  at  one 
time,  unless  expansion  joints  be  provided.  It  is  the  shrink- 
ing of  concrete  that  causes  vertical  cracks  in  plain  con- 
crete walls  to  appear  at  intervals,  and  makes  it  expedient 
to  leave  expansion  joints  in  such  walls  30  ft.  apart  or  so. 
Steel  embedded  in  concrete  walls  or  other  construction 
has  the  effect  of  distributing  the  shrinkage  stresses  and 
lessening  the  shrinkage  cracks,  and  walls  thus  reinforced 
can  be  made  much  longer  without  liability  to  these  cracks 
than  plain  walls.  However,  if  a  long  reinforced  wall  is 
brought  up  uniformly  from  the  ground  up,  shrinkage 
cracks  will  probably  appear.  If  the  wall  be  built  from 
one  end  to  the  other,  allowing  setting  and  shrinkage  of 
part  of  the  wall  before  the  remainder  has  been  placed,  a 
very  long  wall  can  be  made  without  danger  of  these 
185 


cracks.  By  the  same  token  long  concrete-steel  buildings 
should  be  placed  in  alternate  units,  if  much  is  to  finished 
at  once,  leaving  the  intermediate  units  to  be  placed  after 
the  setting  of  the  first;  or  some  other  provision  should 
be  made  to  allow  for  the  shrinkage  of  the  concrete. 

It  is  not  the  intention  here  to  go  into  the  subject  of 
the  making  of  concrete,  more  than  to  say  that  it  is  abso- 
lutely essential  in  this  class  of  work  that  the  concrete  be 
thoroughly  mixed,  and  it  should  be  very  wet.  Dry  or 
mealy  concrete  is  totally  unfit  for  concrete-steel  work.  It 
will  neither  adhere  to  the  steel  nor  protect  it. 

Tests  show  that  a  rod  embedded  in  wet  concrete  will 
resist  pulling  out,  when  the  concrete  has  set  and  hardened, 
with  a  force  of  about  500  Ibs.  per  sq.  in.  of  the  surface  of 
rod  embedded.  At  10,000  Ibs.  per  sq.  in.  on  the  steel  and 
50  Ibs.  per  sq.  in.  adhesion  to  the  concrete  a  round  or 
square  rod  should  be  embedded  50  diameters  in  concrete. 
This  is  very  often  ignored  in  concrete-steel  beams  designed 
for  buildings  and  prepared  for  test.  The  curve  of  maxi- 
mum moments  of  a  beam  taking  uniform  load  or  a  single 
rolling  load  is  a  parabola;  hence  the  curve  of  stress  in  the 
reinforcing  rods,  assuming  them  to  be  parallel  to  the  bot- 
tom of  the  beam,  is  a  parabola.  The  line  representing  the 
adhesive  value  of  a  rod  embedded  in  concrete  is  a  straight 
line  from  the  end  of  rod  to  the  point  of  maximum  stress; 
hence  for  the  adhesive  value  to  be  at  all  sections  greater 
than  the  actual  stress  the  straight  line  should  be  outside 
of  the  parabola;  that  is,  it  should  be  tangent  to  it  at 
the  support.  This  would  make  the  ordinate  of  the  straight 
line  just  twice  that  of  the  parabola,  or  the  adhesive  value 
should  be  double  the  maximum  stress.  Therefore,  it  is 
essential  in  consistent  design  to  have  the  beam  no  less 
than  loo  times  the  diameter  of  rod  from  end  to  center 
of  span.  In  other  words,  the  rod  should  be  no  more  than 
I -200  of  the  span  length. 

Tensile   value   of   the   concrete   should   not   be   allowed 
under  any  circumstance,  as  one  shrinkage  crack  may  de- 
stroy entirely  this  tensile  value  for  the  whole  beam. 
186 


As  intimated,  high  tensile  strains  in  the  steel  though 
they  may  be  warranted  from  the  standpoint  of  high  elastic 
limit  in  the  material,  presume  too  far  upon  the  extensi- 
bility of  the  concrete.  The  elastic  limit  of  ordinary  struc- 
tural steel,  or  40,000  Ibs.  per  sq.  in.?  is  the  most  suitable 
value  to  represent  the  ultimate  useful  strength  of  the  steel. 
With  2,000  Ibs.  per  sq.  in.,  as  the  ultimate  strength  of 
the  concrete  in  compression,  and  with  tension  eliminated 
there  remains  the  variation  of  the  stress  in  the  con- 
crete from  the  neutral  axis  up  and  the  position  of  the 
neutral  axis  to  determine  the  value  of  the  beam  in  flexure. 

Tests  have  shown  that  the  neutral  axis  of  a  concrete- 
steel  beam  remains  close  to  the  middle  of  the  depth  of  the 
beam.  A  little  calculation  will  show  that  a  variation  of 
one-eighth  of  the  depth  of  beam  one  way  or  the  other, 
in  the  standard  construction  here  to  be  proposed,  makes 
a  difference  of  about  6  per  cent  in  the  calculated  resist- 
ing moment,  if  the  stress  in  the  steel  remains  the  same, 
or  about  the  same  difference  if  the  extreme  fiber  stress 
in  the  concrete  remains  the  same.  Using  the  units  here- 
tofore given  and  2,000,000  as  the  modulus  of  elasticity  of 
concrete,  and  substituting  in  one  of  the  elaborate  formulas, 
which  allows  for  parabolic  variation  of  the  stress  in  con- 
crete from  the  neutral  axis  both  ways  and  for  tension  in 
the  concrete,  the  neutral  axis  is  found  to  be  within  4l/2 
per  cent  of  the  middle  of  the  depth  of  the  beam.  So  that 
the  neutral  axis  is  shown,  both  by  theory  and  test,  to  be 
close  to  the  middle  of  the  depth  of  the  beam,  and  its  shift- 
ing a  comparatively  large  fraction  of  the  depth  makes  but 
small  variation  in  the  calculated  strength  of  the  beam. 

The  assumption  that  the  variation  in  stress  in  the  con- 
crete from  the  neutral  axis  to  the  extreme  fiber  is  accord- 
ing to  a  curve  deviating  somewhat  from  a  straight  line 
is  another  element  that  complicates  the  formulas.  Here, 
again,  fine  theory  arrives  at  conclusions  that  are  incom- 
patible with  the  known  variations  in  ultimate  compressive 
strength  of  different  tests  made  of  the  same  materials 

187 


under  apparently  the  same  conditions.  To  assume  that 
the  intensity  of  stress  in  the  concrete  varies  directly  as  the 
distance  from  the  neutral  axis  is  sound  engineering  and 
is  accepted  by  many  investigators. 

In  order  to  simplify  further  the  calculations,  it  is 
recommended  that  the  center  of  the  steel  be  one-eighth 
of  the  depth  from  the  bottom  of  the  beam. 

Referring  to  Fig.  i,  it  is  seen  that  the  total  compres- 
sion in  the  concrete  is 

BD 


2,000 


-=500  BD 


This  must  equal   the  tension   in   the   steel.     Now,   if   the 
area  of  the  steel  be  A,  we  have  40,000  A  =  500  BD,  or  A  = 
1.25  per  cent  of  the  rectangle  BD. 
The  center  of  gravity  of  the  stress  in  the  concrete  is 


above  the  neutral  axis  and  the  effective  depth  of  beam  is 

3 

3  8 

The  ultimate  resisting  moment  is  or 

17 


~>=U-D 

24 


24 


DX  500  BD  or  M=354  BD*. 


Assuming  all  dimensions  in  inches,  this  moment  is  in 
inch-pounds.  Or,  making  B  =  12  and  dividing  by  12 
to  reduce  to  foot-pounds,  we  have  ultimate  bending  mo- 
ment in  foot-pounds  per  foot  in  width  of  slab  or  beam 
=  354  D*. 


Now  as  to  the  shear.  It  is  safe  to  say  that  any  stone 
concrete  that  will  not  stand  50  Ibs.  per  sq.  in.  as  a  safe 
load  in  shear  should  not  enter  into  the  construction  of 
concrete-steel  beams  and  slabs ;  also  that  concrete  should 
not  be  stressed  much  above  this  amount  in  shear.  The 
horizontal  shear  in  the  beam  in  a  section  just  above  the 
rods  is  equal  at  any  point  to  the  increment  of  stress  in  the 
rods.  Hence,  as  we  have  used  the  same  unit  for  shear 
and  adhesion,  there  should  be  the  same  area  across  the 
beam  as  that  of  the  surface  of  the  rods.  Round  rods 
should  then  be  spaced  not  less  than  3.1416  times 
their  diameter  apart  and  square  rods  not  less  than  four 
times  their  diameter  apart;  also  the  distance  to  the  side 
of  beam  at  last  bar  should  not  be  less  than  one-half  of 
these  respective  distances.  With  rods  spaced  just  these 
amounts,  it  will  be  found  that  the  distance  from  center 
of  rod  to  bottom  of  beam  will  be  2*/2  times  the  diameter 
of  rod,  which  is  an  ample  depth  to  insure  gripping  of  the 
steel  by  the  concrete.  Of  course,  rods  can  be  given  wider 
spacing  than  that  shown  in  the  figure.  For  example,  square 
rods  spaced  five  times  their  diameter  apart  will  be  two 
diameters  from  the  bottom  of  beam. 

This  limit  in  the  spacing  of  rods  is  very  often  over- 
looked in  the  designing  of  beams  for  buildings  and  for 
test.  The  beams  are  made  too  narrow  and  unscientific 
expedients  are  resorted  to  to  overcome  the  defect.  This 
has  even  more  force  in  the  case  of  dependence  upon  high 
tension  steel  or  mechanical  bond,  as  the  greater  increment 
of  stress  that  must  be  assumed  demands  greater  area  of 
concrete  to  take  the  horizontal  shear. 

Again,  in  the  matter  of  vertical  shear  at  the  end  of 
span.  Assuming  a  safe  bending  moment  as  one-fourth 
of  the  354  D2  already  found,  and  equating  to  the  expres- 
sion for  the  bending  moment  in  a  uniformly  loaded  beam 
at  W  Ibs.  total  load,  we  have 

WL 
— g— =SSD2(  Z=span  in  fecf) 

189 


But  the  allowed  end  shear  at  50  Ibs.  per  sq.  in.  on  a 
rectangle  12  ins.  wide  and  D  ins.  deep,  remembering  that 
the   maximum   intensity   of   shear   in  a   rectangular   beam 
is  three-halves  of  the  average,  is 
us       9 

MM  o*  *"b   9.^-=—  X50X12  A 

or  total  allowed  load  on  beam  =  W  =  800  D. 

Substituting  this  value  of  W  in  the  equation  above,  we 
have 


88 

But,  as  D  is  in  inches  and  L  is  in  feet,  the  actual  ratio 
is  very  close  to  10.  Hence,  when  the  depth  is  more  than 
one-tenth  of  the  span,  the  full  load  on  a  beam  begins  to 
overtax  the  shearing  strength  of  the  concrete  before  the 
steel  reinforcement  has  its  proper  stress.  Here  again 
some  investigators  have  erred  by  making  short,  deep  test 
beams;  and,  finding  that  they  fail  in  shear,  concluding 
that  concrete  is  inherently  unreliable  in  shear;  whereas 
the  real  fault  is  in  the  design  of  the  beam. 

In  all  concrete-steel  designing  more  or  less  reliance  must 
necessarily  be  placed  upon  the  shearing  strength  of  the 
concrete.  It  only  remains  to  proportion  the  beam  or 
slab  in  such  way  as  to  place  the  concrete  where  it  will 
take  the  shear.  The  best  mechanical  bond  can  do  no  more 
than  transmit  the  forces  of  shear  in  concrete  into  direct 
stress  in  the  steel  or  direct  stress  in  the  steel  into  shear 
in  the  concrete.  It  is  difficult  to  see  how  stirrups  placed 
at  intervals  could  perform  this  function. 

From  Fig.  i  it  is  seen  that  the  maximum  depth  of  beam 
is  20  times  the  diameter  of  rod.  Hence  the  maximum 
ultimate  bending  moment  is 

354  £>~  —  354  X    (20  <*>2  =  U^foo  d* 

But  the  minimum  span  must  be  200  d  to  develop  the 

adhesion  in  the  rod.     This  is  10  times  the  depth,  which 

agrees  with  the  limiting  span  for  shear.     Since  the  shorter 

the  span  the  greater  the  load  per  square  foot  for  the  same 

190 


resisting  moment,  we  may  obtain  the  limiting  load  per 
square  foot  thus :  The  moment  in  foot-pounds  on  a  span 
200  d  -f-  12  ft  long  is 


where  w  is  the  load  per  sq.  ft.  Equating  this  to  141,600 
t/2  we  have  w  —  4,080. 

This  is  the  maximum  ultimate  load  per  sq.  ft.  that  can 
be  placed  upon  the  top  surface  of  a  concrete-steel  beam 
of  stone  concrete  designed  in  the  proportions  here  given 
and  with  the  units  here  employed. 

For  cinder  concrete,  by  the  same  course  of  reasoning, 
using  750  Ibs.  per  sq.  in.  ultimate  compression  and  30 
Ibs.  per  sq.  in.  for  adhesion  and  shear,  we  arrive  at  the 
following  results: 

Maximum  ultimate  bending  moment  =  133  D2. 

Minimum  span  for  adhesion  —  333  d,  or  6.26  D. 

Percentage  of  steel  reinforcement  =  .47. 

Minimum  span  for  shear  =  6.65  X  depth. 

Maximum  ultimate  load  per  square  foot  —  3,910  Ibs. 

It  is  recommended  that  for  quiescent  loads  as  in  build- 
ings a  factor  of  safety  of  3^2  be  used,  and  for  rolling  loads 
a  factor  of  4.  The  minimum  span  lengths,  or,  in  other 
words,  the  maximum  depths,  should  be  used  only  in 
extreme  cases.  In  special  cases,  where  the  beams  would 
be  clumsy,  some  of  the  rods  may  be  curved  up  and  anchored 
at  the  ends,  thus  making  suspension  rods  receiving  all 
of  their  stress  at  the  ends.  A  rod  thus  placed  in  a  curve 
would  carry  the  shear  corresponding  to  its  own  tension, 
leaving  the  concrete  to  take  only  that  due  to  the  trans- 
ference of  stress  into  the  horizontal  rods. 

'  f    I 


^\      ir  .--XL   i 


Fig.  2. 
191 


Fig.  2  shows  the  proportions  for  a  beam  of  this  design. 
The  end  detail  of  the  rod  should  be  capable  of  taking 
practically  all  of  the  stress  on  the  rod;  upsetting  would 
not  be  necessary,  however.  Turning  up  rods  at  the  end 
without  anchoring  the  ends  or  making  them  continuous 
can  scarcely  be  said  to  add  any  useful  element  of  strength. 

The  shear  carried  by  the  curved  rod  will  be  found  to 
be  equal  to  the  stress  in  the  rod  times  H  -r-  l/2  L. 

For  slabs  of  short  span  the  rules  of  design  here  given 
would  demand  close  spacing  of  steel  of  small  diameter. 
Steel  mesh  is  the  most  suitable  material,  if  the  strands  are 
straight;  or  if  wires  or  rods  are  used,  alternate  strips  of 
the  slab  may  be  considered  as  beams  supporting  strips  of 
plain  concrete  between,  which  act  as  fillers,  or  which 
may  be  considered  to  perform  the  useful  office  of  absorb- 
ing shock. 

As  an  example  of  the  application  of  the  foregoing,  given 
a  floor  with  beams  spaced  5  ft.  and  having  a  span  of  20 
ft.  and  these  beams  carried  by  girders  of  the  same  span; 
all  to  carry  100  Ibs.  per  sq.  ft.  of  live  load,  considered  as 
quiescent.  Assume  a  depth  of  slab  of  4  ins.  and  3  ins. 
spacing  of  rods.  The  rod  will  be  l/%  of  the  depth,  or  J^-in. 
from  the  bottom  of  the  slab.  The  safe  bending  moment 
on  the  slab  per  foot  of  width,  with  the  full  area  of  the 
steel,  would  be  101  X  l6  =  J>616  ft.-lbs.  But  the  total 
moment,  including  50  Ibs.  per  sq.  ft.  for  weight  of  slab 
is  150  X  2S  -:-  8  —  469  ft.-lbs.  Hence  in  3  ins.  only 

_^_  of    the    steel    area    is    needed.      Now,    i%    per 
1616 

cent  of  3  X  4  =  -T5  scl-  m-»  anc*  tne  fraction  of 
this  required  is  .044  sq.  in.  One-quarter-inch  round  rods 
will  therefore  suffice.  One-two-hundredth  of  the  span  is 
.3  in.  and  the  diameter  of  rods  is  less  than  this,  as  it  should 
be.  For  the  beam,  assume  a  depth  of  20  ins.  This  includes 
the  depth  of  slab.  Taking  the  dead  load  at  95  Ibs.  per 
sq.  ft.,  the  total  moment  is  5  X  *95  X  2O  X  2°  -r-  8  == 
48,750  ft.-lbs.  The  allowed  moment  on  the  beam  per  foot 
192 


of  width  is  101  X  2O2  =  40,400  ft.-lbs.  The  width  of 
beam  should  therefore  be  1.21  ft.,  or  15  ins.  Rods  will 
be  2  ins.  from  bottom  of  beam,  and  the  area  required  is 
il/4  per  cent  of  300  =  3.75  sq.  ins.  Three  il/s-in.  square 
rods  will  satisfy  the  conditions.  The  maximum  diameter 
of  rod  allowed  = 

JLx240=1.2ins. 
200 

For  the  girders,  assume  a  depth  of  32  ins.,  including 
the  depth  of  slab.  Using  a  dead  load  of  120  Ibs.  per 
sq.  ft.,  the  total  maximum  moment  is  220  X  2O  X  2°2  -f- 
8  —  220,000  ft.-lbs.  The  allowed  moment  per  foot  width 
of  girder  is  101  X  32*=  103,430  ft.-lbs.  The  width  of 
beam  required  is  then  25^  ins.  The  area  of  rods  required 
is  i]/4  per  cent  of  that  of  the  beam,  or  10.2  sq.  ins.  This 
is  very  nearly  made  up  by  six  rods  i%  ins.  in  diameter 
and  two  I  5-16  ins.  The  allowed  safe  shear  on  the  full 
section  of  the  concrete  girder  is  2-3  of  200  (the  nominal 
ultimate)  ~  3l/2  (the  factor  of  safety),  or  40  Ibs.  per 
sq.  in.  The  concrete  will  then  take  40  X  32  X  25-5  — 
32,640  Ibs.  The  total  end  shear  is  44,000  Ibs.  As  the  con- 
crete will  take  just  about  24  of  the  shear,  we  may  turn 
up  the  two  i  5-i6-in.  rods  and  anchor  them  at  the  ends, 
as  in  Fig.  2.  The  stress  in  these  rods  will  be  the  product 
of  their  area  and  2-7  of  40,000  ==  30,930  Ibs.  The  shear 
that  they  will  carry  is  found  by  the  method  given  under 
Fig.  2  to  be  1 1, 680  Ibs.,  which  is  just  about  the  amount 
needed  to  supplement  the  shearing  strength  of  the  concrete. 
The  diameter  of  the  horizontal  rods  is  just  a  trifle  more 
than  1-200  of  the  span  length,  and  the  rods  can  be  spaced 
a  little  more  than  ?r  or  3.1416  times  their  diameter  apart. 
The  two  curved  rods  may  be  placed  between  horizontal 
rods,  as  they  give  rise  to  no  horizontal  shear  in  the  con- 
crete; the  latter  merely  hangs  upon  them  as  a  saddle. 

In  a  beam  of  the  magnitude  of  the  one  just  propor- 
tioned some  saving  of  steel  could  be  effected  by  placing 
the  rods  nearer  to  the  bottom  of  the  beam,  or,  say,  3  ins. 
193 


from  the  same,  and  making  their  area  inversely  propor- 
tional to  the  distance  from  center  of  steel  to  center  of 
compression  in  concrete. 

The  writer  believes  that  the  foregoing  principles  of  de- 
sign, while  they  do  not  show  the  apparent  economy  of 
some  special  systems,  would  place  concrete-steel  designing 
in  the  class  of  sound  engineering  and  force  recognition 
where  it  is  now  decried. 

Tests  of  beams  thus  systematically  designed  would  show 
where  any  modification  of  units  is  needed. 


&'• 

THE  DESIGN  OF  REINFORCED  CONCRETE  BEAMS 
AND  SLABS. 

Sir:  I  have  read  with  great  interest  the  article  by  Mr. 
Edward  Godfrey  on  the  design  of  reinforced  concrete 
beams  and  slabs  in  your  issue  of  March  15,  and  would  say 
that  he  has  handled  the  fundamental  questions  of  the 
subject  with  great  clearness  and  ability.  He  has,  how- 
ever, been  intent  on  simplifying  the  calculations  too  much 
and  thus  fallen  into  the  mistake  of  deriving  empirical 
formulas.  It  seems  to  the  writer  that  it  is  just  as  easy 
to  err  on  one  side  as  the  other  of  mathematical  complexity. 
The  same  path  which  has  been  pursued  in  deriving  for 
steel  beams  working  formulas  which  have  stood  the  test 
of  experiment  and  experience  should  be  followed  here. 
The  fundamental  assumptions,  which  are  the  solid  founda- 
tions of  the  mathematical  edifice,  must  be  carefully  weighed 
and  made  as  broad  and  simple  as  possible.  After  having 
done  this  we  can  proceed  with  full  confidence  that  we  will 
not  be  led  astray  by  a  mathematical  will-o'-the  wisp.  Where 
fanciful  and  complicated  formulas  have  been  derived,  the 
fault  is  not  to  be  found,  as  is  often  too  hastily  assumed,  in 
mathematics  as  such,  but  in  the  lack  of  judgment  or  com- 
mon sense  in  not  starting  aright.  Mathematics  can  be 
compared  to  a  powerful  locomotive  which,  given  a  clear 
track  and  a  cool  brain  to  guide  it,  will  arrive  at  its  desti- 
194 


nation  with  accuracy  and  dispatch,  but  if  put  on  a  poor 
track  and  in  the  hands  of  an  incompetent  runner,  will 
land  in  the  wayside  ditch. 

The  writer  firmly  believes  that  the  mathematical  engine 
has  been  started  correctly  by  Mr.  Paul  Christophe  in  his 
classical  work  on  reinforced  concrete.  The  assumptions 
that  he  starts  on  are  carefully  weighed,  simple  and,  if  I 
may  be  allowed  the  expression,  eminently  sane.  They  are, 
with  modifications  proper  to  the  new  material,  the  same 
as  those  for  the  steel  beam  and  should  therefore  lead  to 
as  satisfactory  results.  As  a  matter  of  fact,  numerous 
experiments  which  have  come  to  the  writer's  knowledge 
bear  this  out.  Not  to  go  into  the  subject  too  deeply  at 
present,  the  writer  would  say  that  the  percentage  of  steel 
for  stone  concrete  of  1.25  per  cent,  which  Mr.  Godfrey  gets, 
is  excessive.  Christophe  demonstrates  that  for  rectangular 
beamr  there  is  a  certain  percentage  of  steel  with  a  cor- 
responding position  of  neutral  axis  and  depth  of  beam 
at  which  both  the  concrete  and  the  steel  are  stressed  up  to 
their  full  respective  values  and  which  is  therefore  the 
economical  one  to  use,  as  both  above  or  below  this  point 
either  the  concrete  or  steel  are  over-stressed.  Taking  the 
depth  of  beams  the  same  as  the  distance  of  the  center  of 
steel  from  the  top  of  beam  (which  is  the  most  rational 
thing  to  do,  we  can  then  add  as  much  or  as  little  concrete 
below  as  other  considerations  will  dictate)  we  get  for  the 
percentage  0.60,  for  the  position  of  neutral  axis  0.385  of 


the  depth  h  and  for  ^0.108  /  ^  where  M  is  the  bend- 
ing moment  and  e  the  width  of  beam.  There  are  several 
other  questions  which  the  writer  would  like  to  take  up  at 
some  other  time.  In  conclusion  he  would  say  that  he 
agrees  with  Mr.  Godfrey  that  correct  principles  of  design 
while  they  do  not  show  the  apparent  economy  of  some 
special  systems,  would  place  concrete-steel  designing  in 
the  class  of  sound  engineering.  There  are  enough  in- 
herently weak  points  in  concrete-steel  as  regards  work- 
105 


manship  and  materials  that  we  should  not  add  further 
uncertainties  caused  by  strenuous  inventors  and  adherents 
of  special  systems.  The  latter  as  a  rule  care  very  little 
for  advancing  the  cause  of  good  engineering  as  long  as 
they  can  make  it  pay  and  cases  are  liable  to  arise  where 
twisting  and  even  falsification  of  facts  may  be  resorted  to 
in  order  to  keep  an  otherwise  discredited  system  in  ap- 
parently good  repute.  Yours  truly, 

Henry  Szlapka, 

Resident  Engineer,  Toledo-Massillon  Bridge  Co. 
342  Mint  Arcade,  Philadelphia,  Pa.,  March  30,  1906. 


Sir:  I  am  in  receipt  of  proof  of  a  letter  to  you  from 
Mr.  Henry  Szlapka,  criticising  my  article  on  the  design 
of  reinforced  concrete  beams  and  slabs,  published  in  your 
issue  of  March  15,  and  desire  to  thank  you  for  this  op- 
portunity to  reply  to  the  same. 

The  first  word  that  strikes  me  as  strange  in  this  letter 
is  the  word  empirical,  as  applied  to  my  formula.  Em- 
pirical is  defined  as  pertaining  to  or  derived  from  experi- 
ment. In  the  sense  that  unit  values,  and  sometimes  final 
results,  in  formulas  for  strength  must  be  derived  from 
experiment,  all  such  formulas  might  be  classed  under  this 
head.  But  as  commonly  employed  the  term  means  a  more 
or  less  scientific  guess.  The  formula  I  derive  is  not  em- 
pirical, for  it  is  derived  from  the  well-known  theory  of 
beams,  using  the  strength  of  steel  and  concrete  as  deter- 
mined from  tests,  and  a  position  of  the  neutral  axis  deter- 
mined from  tests  to  locate  the  neutral  axis  (not  by  the 
uncertain  method  of  using  comparative  moduli  of  elastic- 
ity). Mr.  J.  J.  Harding,  in  a  paper  read  before  the  West- 
ern Society  of  Engineers,  Oct.  25,  1905,  says,  "Experimental 
methods  are  desirable  for  determining  the  position  of  the 
neutral  axis,  as  it  enables  one  to  design  a  beam  without 
making  an  assumption  as  to  the  modulus  of  elasticity  of 
the  concrete,  which  may  easily  vary  100  per  cent." 

For  the  sake  of  simplicity   I  have   eliminated  some  of 

196 


the  unnecessary  kinks  in  the  other  formulas.  For  ex- 
ample,  I  have  represented  the  stress  in  the  concrete  by 
a  triangle  and  not  by  a  triangle  with  a  little  segment 
added  to  the  hypothenuse.  The  strength  of  concrete  is 
not  so  well  defined,  even  if  conditions  of  manufacture 
and  the  materials  appear  to  be  identical,  as  to  make  it 
expedient  to  count  in  the  almost  insignificant  segment  of 
force  with  all  of  the  complexity  it  entails  in  the  formula, 
granting  for  the  sake  of  the  argument  that  the  compres- 
sion in  the  concrete  does  not  vary  as  the  distance  from 
neutral  axis.  Suppose  it  should  be  discovered  by  use  of 
exceedingly  delicate  instruments  that  steel  under  various 
stresses  has  a  sliding  modulus  of  elasticity,  then  the 
principle  of  the  design  of  beams  that  the  extension  or 
shortening  of  the  fibers  varies  directly  as  the  stress  would 
not  be  exactly  correct,  and  the  stress  would  not  vary  in 
intensity  exactly  as  the  distance  from  the  neutral  axis, 
but  as  the  ordinates  to  some  curve.  Now  there  is  no 
doubt  at  all  that  some  mathematician  would  arise,  with 
lots  of  time  at  his  disposal,  who  would  work  out  a  gen- 
eral formula  to  take  this  variation  into  account  for  all 
shapes  of  beams.  A  difference  in  the  strength  of  beams 
might  be  found  amounting  to  one  or  more  per  cent.  The 
strength  of  one  bar  of  steel  tested  at  two  different  places 
may  vary  several  per  cent,  and  the  opinions  of  two 
engineers  as  to  the  proper  factor  of  safety  may  vary  still 
more;  but  this  does  not  concern  the  mathematician,  who 
has  found  a  principle  of  mathematics  violated  by  the  com- 
monly used  "empirical"  formula.  Now  I  do  not  want  to 
place  a  practical  designer  like  Mr.  Szlapka  in  a  class 
with  this  mathematician,  but  I  want  to  say  that  there  is 
a  lot  of  mathematical  dust  thrown  into  the  eyes  of  de- 
signers who  have  not  the  time  or  the  inclination  to  delve 
into  these  abstruse  mathematical  questions,  but  who  would 
like  at  the  same  time  to  know  a  sound  reason  for  using 
a  formula,  and  to  have  that  formula  stripped  of  all  elements 

197 


that  complicate  it  without  introducing  any  useful  additional 
element  of  correctness. 

As  to  i%  per  cent  of  steel  being  too  high,  I  quote  from 
Prof.  A.  N.  Talbot  in  Engineering  News,  July-December, 

1904,  page   125 :     "For   1:3:6  concrete,  reinforcement  as 
high  as   il/2  per  cent  for  steel  of  33,000  Ibs.  per  sq.   in. 
elastic  limit     *     *     *     may   be   used   without   developing 
the  full  compressive  strength  of  the  concrete."     The  pro- 
portions of  concrete  that  I  recommend  are  1:2:4,  a  much 
stronger  concrete,  generally,  than  1:3:6;  it  would  allow 
a  greater  percentage  of  steel.     Again,  to  quote  Prof.   W. 
Kendrick  Hatt  in  "Engineering  Record,"  Vol.  51,  page  545: 
"In  the  writer's  tests  of  beams  under  a  center  load,  2l/2 
per  cent  steel  failed  to  develop  the  crushing  strength  of 
the  concrete."     In  Engineering  News  of  Feb.  15,  1906,  p. 
170,  Mr.  J.  J.  Harding  states  that  for  steel  of  an  elastic 
limit  of  35,000  Ibs.  he  would  use  between  i  and  i*4  per  cent 
of  the  area  of  the  concrete.    Mr.  T.  L.  Condron,  in  a  paper 
read  before  the  Western  Society  of  Engineers,  March  15, 

1905,  says:     "For   extra   strong   concrete   of   about    i    of 
cement,  2  of  sand  and  4  of  broken  stone,  the  percentage 
of  reinforcing  may  be  increased  to  1.25  per  cent."     (This 
in  a  discussion  of  202  tests.)      In  view  of  the  foregoing 
conclusions  from  the  results  of  tests  it  is  hard  to  see  the 
force  of  Mr.  Szlapka's  bald  assertion  that  i1/^  per  cent  is 
excessive. 

Mr.  Szlapka  also  objects  to  my  assumption  that  the 
neutral  axis  is  in  the  middle  of  the  depth  of  concrete.  As 
intimated,  this  was  done  on  the  strength  of  the  results 
of  tests  or  measurements  to  locate  the  neutral  axis  and 
not  by  means  of  a  fancy  formula,  though  it  is  not  at 
variance  with  one  of  the  most  complex  formulas  I  could 
find.  In  Engineering  News,  July-December,  1904,  pp. 
124-125,  Prof.  Talbot  gives  plottings  of  the  position  of  the 
neutral  axis.  For  1.39  per  cent  reinforcement  the  distance 
from  top  of  beam  is  almost  exactly  50  per  cent  of  the  depth 
from  top  of  concrete  to  steel.  For  0.97  per  cent  it  is  about 

198 


0.42  of  the  same  depth.  Prof.  Talbot  gives  this  formula 
for  finding  the  position:  k  —  0.26  +  0.18  p,  where  k  is 
the  fraction  of  depth  from  top  to  neutral  axis,  and  /> 
is  the  percentage  of  steel.  For  i1/^  per  cent  this  would 
be  0.485  of  depth  from  top  of  concrete  to  steel.  Prof.  F. 
E.  Turneaure  in  Engineering  News,  July-December,  1904, 
p.  215,  says:  "The  diagrams  show  the  neutral  axis  to  lie 
at  first  very  near  the  center  of  the  concrete  beam.  As  the 
cracks  develop  it  moves  gradually  nearer  to  the  compres- 
sion side." 

The  use  of  the  term  "depth  of  beam"  to  designate  the 
distance  from  top  of  concrete  to  steel  is  merely  a  mat- 
ter of  nomenclature.  There  are  good  practical  reasons  for 
using  the  outside  depth  of  concrete  as  the  "depth."  In 
the  first  place  it  figures  in  the  mind  of  the  designer  as 
the  depth  and  governs  the  clearance,  and  it  is  usually  in 
round  numbers.  In  the  second  place  a  rule  such  as  I 
give  requiring  l/%  of  the  depth  from  center  of  steel  to  bot- 
tom of  beam  gives  sufficient  concrete  below  the  steel  to 
grip  it  and  does  not  admit  of  skimping  in  this  respect. 
It  is  a  very  essential  point  of  design  that  the  steel  be  sur- 
rounded with  enough  concrete  to  grip  it  effectually.  This 
is  a  point  often  overlooked  in  designing. 

It  has  not  been  my  purpose  to  discredit  mathematics 
but  to  point  out  the  fallacy  of  unnecessary  complication 
in  formulas  for  use.  In  the  struggle  for  existence  the 
fittest  formula  has  generally  been  found  to  be  the  simplest. 
Yours  very  truly, 

Edward  Godfrey. 
Monongahela  Bank  Building,  Pittsburg,  Pa.,  April  12,  1906. 


THE  DESIGN  OF  REINFORCED  CONCRETE 
BEAMS  AND  SLABS 

Sir:  The  writer  asks  for  the  privilege  of  presenting  a 
reply  to  Mr.  E.  Godfrey's  letter  in  your  issue  of  May  3, 
not  for  the  sake  of  continuing  a  discussion  and  sparring 


for  the  last  word,  but  because  many  points  are  raised 
of  an  exceedingly  practical  character,  on  which  the  writer 
earnestly  seeks  for  light.  If  Mr.  Godfrey's  statement  that 
1%  per  cent  is  the  proper  amount  of  steel  reinforcement 
is  correct,  then  the  writer  is  wrong  by  over  100  per  cent 
and  naturally  feels  great  uneasiness  over  the  safety  of 
numerous  structures  which  he  has  designed,  and  which  have 
been  built  on  his  theory.  His  only  justification  must  be, 
that  he  has  erred,  not  through  carelessness,  but  through 
unavoidable  ignorance  which  is  shared  by  a  great  number 
of  his  colleagues.  He  would  like  to  ask  Mr.  Godfrey  and 
beyond  him,  all  practical  designers  who  may  notice  this 
letter,  whether  they  have  used  a  percentage  of  i^J  or  one 
nearer  0.60  in  their  actual  work.  If  they  have  used  the 
former,  they  were  more  fortunate  than  the  writer  in  not 
having  had  to  meet  close  commercial  competition. 

A  great  number  of  times  estimates  made  on  the  writer's 
theory  have  been  beaten  by  reputable  rivals  and  those  of 
his  designs  which  were  executed  did  not  differ  by  any 
material  amount  from  other  plans.  The  sizes  given  by 
his  theory  have  usually  compared  closely  with  those  by 
other  more  competent  designers  and,  moreover,  have  passed 
the  careful  scrutiny  of  building  inspectors.  If  he  is 
radically  wrong,  he  can  only  regret  that  he  did  not  follow 
the  advice  of  one  of  the  best  known  bridge  engineers  given 
some  years  ago,  who  told  him  that  he  was  too  young  to 
risk  his  reputation  by  dabbling  with  reinforced  concrete, 
because  in  the  course  of  time  such  structures  would  develop 
numerous  flaws  as  yet  hidden  from  observation.  As  a 
matter  of  fact,  a  concrete  engineer  has  to  take  too  many 
chances  from  poor  materials  and  lack  of  care  in  execution 
of  his  work  to  add  deliberately  another  grave  risk  of 
error  from  theory.  Where  so  much  uncertainty  exists,  he 
must  accept  the  best  current  practice,  select  the  most 
reasonable  theory  as  a  basis  for  his  designs  and  await  the 
consequences,  assured  that  he  cannot  be  held  morally  re- 
sponsible for  defects  which  could  not  be  prevented  by  using 
200 


all  due  precaution.  The  case  would  be  different  with  a 
designer  who  use  gross  section  instead  of  net  of  the  steel 
reinforcement  with  the  intention  of  making  his  customer 
believe  he  was  getting  more  than  he  actually  received.  This 
is  a  matter  in  which  ignorance  cannot  be  excused. 

Mr.  Godfrey  takes  up  considerable  space  in  combating 
statements  never  made  by  the  writer,  which  cover  points 
on  which,  as  a  matter  of  fact,  they  are  in  agreement,  as 
will  be  shown.  He  also  talks  about  "mathematical  dust" 
and  "bald"  statements.  The  "mathematical  locomotive" 
naturally  raises  a  great  deal  of  dust  in  its  flight  through 
spacej  like  its  material  prototype,  but  that  is  a  by-product 
which  need  not  concern  the  man  at  the  throttle.  It  can 
be  left  to  be  gathered  up  by  the  poor  professional  mathe- 
maticians, for  whom  most  engineers  profess  such  a  marked 
contempt.  As  to  baldness,  the  writer  does  not  worry 
about  being  in  that  incipient  condition  himself,  but  feels 
very  much  concerned  about  his  statements  having  reached 
that  stage. 

To  bring  matters  to  a  definite  issue  the  writer  will 
briefly  state  the  fundamental  assumptions  of  Mr.  Chris- 
tophe's  theory  and  ask  Mr.  Godfrey's  and  others'  opinion, 
why  in  the  present  state  of  the  art  they  are  not  the  best, 
avoiding  unnecessary  refinement  on  the  one  hand,  and 
being  sufficient  on  the  other  to  serve  as  a  broad  basis  for 
elaboration.  If  they  are  correct,  the  writer  feels  no  hesita- 
tion in  following  wherever  they  lead  to.  These  assump- 
tions are  five  in  number:  (i)  Solidarity  of  concrete  and 
reinforcement,  provided  the  latter  is  so  arranged  as  to 
assure  a  sufficient  bond  between  the  two;  (2)  invariability 
of  plane  sections;  (3)  invariability  of  the  coefficient  of 
elasticity  of  concrete  in  compression  within  the  usual  limits 
of  stress;  (4)  neglecting  the  action  of  concrete  in  tension; 
(5)  absence  of  initial  stresses. 

Mr.Godfrey  speaks  in  all  cases  of  ultimate  values,  whereas 
the  ordinary  theory  does  not  pretend  to  follow  beyond 
the  elastic  limit,  either  in  steel  or  in  concrete  steel,  and 

201 


it  therefore  seems  that  results  deduced  from  testing  beams 
to  failure  have  little  value  as  interpreted  by  our  ordinary 
formulas.  Moreover,  beams  of  rectangular  section,  which 
are  the  only  ones  fully  discussed  in  textbooks  and  experi- 
mented on,  are  very  little  used  in  actual  practice  as  com- 
pared with  beams  of  T  section  where  the  floor  slab  is 
counted  on  for  part  of  the  compression  flange.  What  per- 
centage of  steel  would  Mr.  Godfrey  fix  on  for  that  case? 

As  to  the  writer's  definition  of  "depths  of  beam"  it  is 
the  only  rational  one  to  use,  even  if  this  statement  is 
bald.  Take  a  shallow  beam,  say  8  ins.  deep  and  a  deep 
one,  say  36  ins.,  both  within  practical  everyday  limits. 
In  the  one  case  Mr.  Godfrey  would  get  I  in.  and  in  the 
other  4^2  ins.  for  the  amount  of  concrete  under  steel. 
Would  he  actually  use  these  figures  in  a  commercial  de- 
sign? This  amount  will  rather  be  found  to  be  a  constant 
and  that  because  of  a  very  important  consideration  which 
Mr.  Godfrey  has  not  touched  on.  That  is  the  protection 
afforded  against  fire,  and  here  a  great  diversity  of  opinion 
exists.  Prof.  Chas.  L.  Norton,  as  quoted  in  Taylor  & 
Thompson's  book  on  concrete,  considers  2  ins.  in  all 
beams  and  girders  essential  and  most  building  regulations 
call  for  at  least  that  amount.  However,  no  more  than 
il/£  ins.  has  been  used  very  often  and  passed  by  some 
building  departments.  In  a  fire  test  of  a  system  which 
has  never  used  more  than  that  amount  it  was  incresed 
to  2l/t  ins.,  for  the  purpose  of  the  test  only,  according  to 
the  writer's  best  knowledge  and  belief.  There  is  also 
another  point  in  this  connection  which  has  not  been  com- 
mented on,  and  which  deserves  careful  consideration.  In  or- 
der to  attach  shafting  or  pipes  to  reinforced  concrete  beams, 
many  different  devices  have  been  used,  among  others  some 
in  which  a  socket  or  similar  device  is  in  close  contact  with 
the  reinforcement.  In  case  of  fire,  heat  is  thus  trans- 
mitted directly  to  the  steel  reinforcement  with  the  result 
of  heating  it  rapidly  and  causing  the  concrete  protection 
to  fall  off,  due  to  the  unequal  expansion,  the  concrete  taking 
202 


a  much  longer  time  to  heat  to  the  same  temperature  than 
the  steel;  therefore,  such  devices  should  not  be  allowed, 
or,  if  they  are,  the  buildings  so  constructed  should  not 
be  held  up  as  examples  of  fireproof  construction.  The 
last  two  points  mentioned  have  apparently  been  frequently 
overlooked,  but  should  not  be  slighted  in  the  future. 

If  the  inventor  of  a  system  is  compelled  to  use  features 
which  cannot  comply  with  scientific  requirements  and  tries 
to  pass  them  off  under  the  sanction  of  the  building  depart- 
ment of  a  prominent  city,  he  is  no  better  than  the  packer 
of  poisoned  meat  who  uses  the  apparent  sanction  of  United 
States  government  inspection  which,  when  closely  investi- 
gated, has  no  substantial  meaning,  but  of  which  fact  the 
public  knows  nothing. 

As  stated  before,  there  are  enough  unavoidable  uncer- 
tainties* in  the  subject  without  adding  other  difficulties  of 
our  own  making.  In  the  rebuilding  of  San  Francisco  rein- 
forced concrete  will  play  an  important  part,  but  grave 
fear  must  be  entertained  that  unscrupulous  competition 
will  result  in  much  reckless  and  "skinned"  work,  unless 
held  in  check  by  regulations  and  inspection  which  are 
more  than  a  mere  name.  Yours  truly, 

Henry  Szlapka,, 
Res.  Engr.  Toledo  Massillon  Bridge  Co. 

342  Mint  Arcade,  Phila.,  May  7,  1906. 

The  author  did  not  reply  to  the  above  letter  of  Mr. 
Szlapka.  The  letter  does  not  bring  out  much  that  is  new. 
As  to  Christophers  assumptions,  No.  (5)  would  not  hold 
in  ordinary  beams,  as  the  shrinking  of  the  concrete  does 
put  initial  stress  in  the  steel,  and  this  disturbs  all  assump- 
tions about  the  coefficients  of  elasticity,  including 
No.  (3),  as  made  use  of  to  locate  the  neutral  axis. 
As  to  the  amount  of  concrete  that  is  proper  to  use  below 
the  steel,  it  would  not  be  reasonable  to  use  the  same  amount 
below  a  wire  mesh  in  a  slab  as  would  be  needed  below 
and  around  a  round  or  square  bar  2  in.  or  so  in  diameter. 
The  concrete  is  needed  to  grip  as  well  as  protect  the  steel, 

203 


and  light  sections  of  steel  do  not  need  as  much  concrete 
to  grip  them  as  heavy  sections;  also  light  sections  do  not 
need  as  much  protection  as  heavy  ones,  because  they  are 
of  less  importance  in  the  structure.  One  inch  of  concrete 
is  sufficient  in  a  shallow  slab.  It  is  totally  inadequate  in  a 
large  beam  with  heavy  rods. — [AUTHOR.] 


The  Design  of  Reinforced  Concrete 
Columns  and  Footings. 

INTRODUCTION.— In  the  paper  published  in  En- 
gineering News  of  March  15,  1906,  the  writer  derived 
some  simple  formulas  for  the  design  of  reinforced  concrete 
beams  and  slabs  and  some  rules  governing  the  proper  pro- 
portioning of  the  steel  for  reinforcement  and  the  limiting 
span  length.  Accepting  the  premises  given  in  that  paper, 
it  becomes  a  simple  matter  to  design  beams  and  slabs  in 
this  comparatively  new  combination  of  materials.  There 
seems  to  be  no  voice  lifted  up  to  deny  the  complete  safety 
of  beams  thus  designed  to  carry  their  loads,  and  no  sub- 
stantiated objection  to  the  proposed  method  of  design  has 
yet  been  raised  on  the  side  of  economy — the  other  end  of 
the  see-saw  that  the  engineer  must  maintain  in  equilibrium. 

Many  so-called  practical  tests  have  been  made  on  rein- 
forced concrete  construction  in  place  that  do  not  merit 
the  name  of  tests.  They  are  made  on  a  small  section  of 
a  floor  supported  on  all  sides  by  the  contiguous  construc- 
tion, and  do  not  test  in  any  adequate  sense  the  part  of  the 
floor  immediately  loaded.  If  a  designer  of  steel  construc- 
tion should  load  a  beam  by  placing  a  uniform  load  on  a 
fraction  of  its  length  and  declare  that  from  the  results  of 
the  "test"  the  beam  is  shown  to  be  capable  of  carrying 
that  uniform  load  throughout,  he  would  be  promptly  ruled 
out ;  and  yet  this  is  the  kind  of  test  that  is  commonly  held 
up  as  demonstrating  the  ability  of  some  forms  of  con- 
crete-steel design  to  carry  enormous  loads.  Careful  tests 
of  isolated  beams  have  been  made  in  large  numbers,  which 
204 


have  proven  with  practical  agreement  the  correctness  of 
the  premises  and  rules  of  proportion  as  well  as  the  re- 
.  suiting  formulas  obtained  by  the  writer  in  the  paper  above 
referred  to. 

On  account  of  inquiries  and  criticisms  that  the  writer 
has  received  from  different  sources,  it  is  thought  to  be  in 
place  to  amplify  the  former  paper  on  beams  and  slabs  by 
what  immediately  follows. 


X 


Fig.  1. 

Tests  have  shown  that  rods  of  a  greater  diameter  than 
about  i -200  of  the  span  are  apt  to  pull  out  of  the  concrete 
without  breaking,  on  account  of  the  lack  of  length  in  con- 
crete to  grip  the  metal  effectually.  Other  tests  have  shown 
that  beams  having  a  greater  depth  than  one-tenth  of  the 
span  and  containing  horizontal  rods  at  the  bottom,  or 
having  rods  turned  up  at  the  support  and  not  anchored  at 
the  ends,  will  fail  when  loaded  to  destruction,  approxi- 
mately as  per  sketch  Fig.  I.  This  demonstrates  the  in- 
ability of  the  concrete  in  beams  so  designed  to  carry  the 
end  shear,  vertical  and  horizontal  (which  combine  in  the 
diagonal  line  in  the  figure),  when  the  depth  exceeds  one- 
tenth  of  the  span. 

On  the  location  of  the  neutral  axis,  theoretical  methods 
of  determining  its  position  by  the  relative  moduli  of  elas- 
ticity of  steel  and  concrete  are  unsatisfactory,  on  account 
of  the  wide  variation  in  the  modulus  of  elasticity  of  con- 
crete as  determined  by  compression  tests.  There  is,  how- 
ever, a  more  direct  method  of  locating  this  axis,  and  one 
which  gives  more  concordant  results,  namely,  by  measur- 
ing the  relative  extension  and  shortening  of  the  lower  and 
upper  fibres  in  a  beam  under  test.  In  a  letter  replying  to 
a  critic  on  this  phase  of  the  subject  the  writer  gave  the 
205 


following  defense  of  his  position,  which  is  here  repeated 
to  make  this  paper  complete  for  reference: 

"In  Engineering  News,  July-December,  1904,  pp.  124- 
125,  Prof.  Talbot  gives  plottings  of  the  position  of  the 
neutral  axis.  For  1.39  per  cent  reinforcement  the  distance 
from  top  of  beam  is  almost  exactly  50  per  cent  of  the  depth 
from  top  of  concrete  to  steel.  For  0.97  per  cent  it  is  about 
0.42  of  the  same  depth.  Prof.  Talbot  gives  this  formula 
for  finding  the  position:  k  =  0.26  +  0.18  p,  where  k  is  the 
fraction  of  the  depth  from  top  to  neutral  axis  and  p  is 
the  percentage  of  steel.  For  1%.  per  cent  this  would  be 
0.485  of  the  depth  from  top  of  concrete  to  steel.  Prof. 
F.  E.  Turneaure  in  Engineering  News,  July-December,  1904, 
p.  215,  says:  The  diagrams  show  the  neutral  axis  to  lie 
at  first  very  near  the  center  of  the  concrete  beam.  As  the 
cracks  develop  it  moves  gradually  nearer  to  the  compres- 
sion side.' " 

On  the  proper  percentage  of  steel  the  writer's  paper  was 
also  criticised  by  the  person  to  whom  the  reply  in  the  last 
paragraph  was  directed.  This  critic  stated  that  1%  per 
cent  is  too  large  a  percentage  of  steel.  This  criticism  is 
correlative  with  the  one  on  the  location  of  the  neutral 
axis.  A  higher  location  of  that  axis  means  a  less  per- 
centage of  steel,  since  it  affords  a  larger  lever  arm  or 
effective  depth  in  the  resisting  moment.  The  writer's  reply 
to  this  criticism  was  as  follows:  "As  to  i%  Per  cent  being 
too  high,  I  quote  from  Prof.  A.  N.  Talbot,  in  Engineering 
News,  July-December,  1904,  page  125 :  Tor  1:3:6 
concrete,  reinforcement  as  high  as  il/2  per  cent  for  steel 
of  33,000  Ibs.  per  sq.  in.  elastic  limit  *  *  *  may  be  used 
without  developing  the  full  compressive  strength  of  the 
concrete.' "  The  proportions  of  concrete  that  I  recom- 
mend are  I  :  2  :  4,  a  much  stronger  concrete,  generally, 
than  I  :  3  :  6;  it  would  allow  a  greater  percentage  of 
steel.  Again,  to  quote  Prof.  W.  Kendrick  Hatt,  in  "En- 
gineering Record,"  Vol.  51,  page  545:  "In  the  writer's 
tests  of  beams  under  a  center  load  2j4  per  cent  of  steel 
206 


failed  to  develop  the  crushing  strength  of  the  concrete." 
In  Engineering  News  of  Feb.  15,  1906,  page  170,  Mr.  J.  J. 
Harding  states  that  for  steel  of  an  elastic  limit  of  35,000 
Ibs.  he  would  use  between  I  and  iJ4  per  cent  of  the  area 
of  the  concrete.  Mr.  T.  L.  Condron,  in  a  paper  read  be- 
fore the  Western  Society  of  Engineers,  March  15,  1905, 
says :  "For  extra  strong  concrete  of  about  I  of  cement, 
2  of  sand  and  4  of  broken  stone,  the  percentage  of  rein- 
forcement may  be  increased  to  1.25  per  cent."  (This  in  a 
discussion  of  202  tests.) 

The  writer  has  been  asked  why  he  does  not  use  the  floor 
slab  in  connection  with  the  beam  as  top  flange,  making  a 
tee  beam  out  of  it.  The  buckle  plate  in  a  steel  floor  would 
not  be  used  as  top  flange  of  the  floor  beams,  though  it  may 
be  secured  firmly  to  the  beams;  and  there  is  no  good  rea- 
son for  using  the  concrete-steel  floor  slab  as  part  of  the 
beam.  The  slab  is  spread  out  too  much  for  a  proper  dis- 
tribution of  the  stresses,  and  it  may  have  holes  cut  into  it 
for  pipes,  etc.,  thus  destroying  its  value  as  beam  flange. 
Again,  to  include  it  in  the  calculations  would  add  largely 
to  the  percentage  of  steel  in  the  lower  half  of  the  rectangle 
of  the  beam.  The  rectangle  of  the  concrete  should  not  be 
called  upon  to  take  care  of  more  than  about  1^4  Per  cent 
of  steel.  Practically  the  only  saving  effected  by  counting 
in  the  slab  is  in  the  amount  of  concrete  in  the  lower  part 
of  the  beam.  The  concrete  is  needed  there  to  protect  the 
steel  against  corrosion  and  fire,  and  generally  to  give  width 
enough  to  the  beam  to  take  care  of  the  horizontal  shear. 

The  subject  of  the  limiting  load  that  a  concrete-steel 
beam  of  the  proportions  given  in  the  former  paper  may 
carry  may  be  amplified  as  follows :  Assuming  the  neutral 
axis  of  a  beam  to  remain  in  the  middle  of  its  depth  for 
safe  loads,  it  is  seen  that  the  safe  resisting  moment  of  the 
beam  is  directly  proportional  to  the  amount  of  steel.  For 
steel  in  less  amounts  than  1^4  Per  cent  tne  stress  in  the 
concrete  is  less  than  2,000  Ibs.  per  sq.  in.  at  40,000  Ibs. 
per  sq.  in.  on  the  steel,  but  cases  may  arise  where  it  is 
207 


more  economical  to  increase  the  relative  amount  of  con- 
crete. If  the  depth  of  a  beam  be  doubled,  its  resisting 
moment  per  foot  of  width  will  be  four  times  as  great, 
assuming  that  the  steel  is  still  i^4  per  cent;  that  is,  that 
the  steel  is  doubled  also.  Now,  if  the  amount  of  steel  in 
the  beam  of  double  depth  be  divided  by  two,  the  resisting 
moment  will  be  one-half  as  great.  In  other  words,  if  the 
same  rods  be  used  in  a  beam  of  twice  the  depth,  the  re- 
sisting moment  is  doubled.  The  weight  of  the  concrete 
and  the  depth  of  the  beam  are,  of  course,  twice  the  values 
in  the  original  beam,  and  these  may  be  objectionable,  when 
the  double  strength  could  be  obtained  by  using  a  beam  1.4 
times  as  deep,  with  i^4  per  cent  of  steel.  However,  where 
a  large  increase  in  depth  and  weight  of  concrete  are  not 
objectionable,  the  limiting  ultimate  load  of  4,080  Ibs.  per 
sq.  ft.  on  the  top  surface  of  the  beam  may  be  increased 
without  necessitating  the  curving  up  and  anchoring  of 
some  of  the  rods.  Thus,  if  the  limiting  beam  of  one-tenth 
of  the  span  be  doubled  in  depth,  with  the  same  steel,  it 
will  have  twice  the  strength  and  also  twice  the  shearing* 
area  at  the  ends;  hence  it  will  have  twice  the  ultimate 
capacity.  In  the  foregoing  the  ratio  in  depth  of  one  to 

two  is  taken  to  simplify  the  discussion.    Any  other  relative 

• 

:cpi  anil 
ad* 


representing  Grip  or  Adhesion  of  Pod 
of  Moments 


. 

depths  could  be  taken,  and  it  would  be  found  that  starting 


with   any   given   beam   having 

208 


per   cent   of   steel   the 


strength  of  a  deeper  beam  of  the  same  width  with  the 
same  steel  rods,  placed  l/%  of  the  depth  from  the  bottom, 
will  be  directly  as  the  depths. 

DESIGN  OF  COLUMN  AND  WALL  FOOTINGS.— 
In  proportioning  concrete-steel  footings  the  same  prin- 
ciples of  design  hold;  the  beam,  however,  is  a  cantilever 
and  not  a  simple  beam. 

Given  a  wall  footing  with  a  projection  p  and  an  upward 
pressure  of  the  soil  of  S  tons  per  square  foot;  in  order 
to  have  shearing  area  at  the  '  edge  of  wall  to  take  the 
upward  pressure  on  the  projection  p,  at  40  Ibs.  per  sq. 
in.  on  the  gross  area,  we  have 


144 
or  h  =  .35  />  S  ...................  (i) 

That  is,  for  every  ton  of  soil  pressure  per  square  foot 
there  must  be  a  height  h  of  0.35  times  p.  Square  rods 
seem  to  be  the  most  suitable  for  footings.  For  the  size 
of  rod,  in  order  to  have  50  diameters  of  the  rod  in  con- 
crete at  the  point  of  maximum  stress  it  is  necessary  to 
use  rods  of  a  diameter  not  greater  than  1-50  of  the  pro- 
jection p.  The  curve  of  moments  and  of  stress  in  the  rods 
is  a  parabola  which  lies  at  all  points  within  the  straight 
line  representing  the  adhesion  or  gripping  of  the  rod  by 
the  concrete.  Hence  p  need  be  no  greater  than  50  d.  As- 
sume that 

P  =  50  d  .........  .........  (2) 

and  that  the  stress  on  steel  is  12,500  Ibs.  per  sq.  in.  The 
amount  of  stress  on  the  concrete  will  be  the  same  as  that 
on  the  steel,  hence  we  may  write  for  the  allowed  moment 
on  the  section  x  inches  in  width  and  h  inches  in  depth, 

M=12,SQO  d2  X—  £=8,854  d2  h% 
24 

But  h  —  .35  p  S,  whence  M  =  3,099  p  d2S  inch-lbs. 
For  the  upward  pressure  of  S  tons  per  sq.  ft.  we  have 


209 


Equating  these  two  values  of  M  and  using  for  p  its  value 

50  d  we  have  ^  W 

x  =  8.93  d,  or  say  9  d  ......  ........  ....(3) 

Hence  for  any  upward  pressure  the  same  rods  would 
be  used,  having  a  diameter  1-50  of  p  and  spaced  9  times 
their  diameter  apart.  Only  the  height  h  would  vary  for 
different  earth  pressures,  as  per  equation  (i). 

The  foregoing  does  not  take  into  account  the  stress  on 
the  concrete,  but  we  have  seen  that  when  the  steel  does 
not  exceed  i%  per  cent  of  the  concrete  the  stress  in  the 
concrete  will  not  be  excessive.  When  the  steel  in  this  foot- 
ing =  i%  per  cent  of  the  concrete, 

£=8.89  </or 


50 

This  would  mean  an  earth  pressure  of  only  about  a  half 
a  ton  per  square  foot.  Hence  for  all  practicable  earth 
pressures  the  amount  of  concrete  is  ample.  ,  '  * 

In  square  footings  for  columns  the  corners  will  have  a 
projection  1.4  times  that  of  the  sides.  The  height  h 
should  be  made  1.4  times  that  obtained  by  equation  (i) 
using  the  projection  at  the  side.  Some  rods  should  be 
laid  diagonally,  as  shown  in  Fig.  3. 


to   ii  Fig-  3- 

If  cinder   concrete  be  used   in  the  wall  footing,   at  25 
Ibs.  per  sq.  in.  shear  on  gross  area,  we  have 

p  =  83  d (4) 

h  =  .&Sp (5) 

x  =  8.5  d, (6) 

210 


For  a  plain  concrete  footing  in  stone  concrete,  allowing 
40  Ibs.  per  sq.  in.  as  safe  modulus  of  transerve  strength 
we  have  for  the  bending  moment  under  edge  of  wall 
2,000  3^  f* 
144"       2 

and  for  the  resisting  moment  52-1"    both  on  a  rectangle  h 

6    ' 

inches  deep  and  one  inch  wide.     Equating  these  we  find 
the   following   to   be   very   nearly   true: 

S  p*  =  h* (7) 

For  a  plain  cinder  concrete  footing  at  20  Ibs.  per  sq. 
in.  safe  modulus  of  transverse  strength,  similarly  we  find 

2$  p*  =  h2 (8) 

By  the  .foregoing  we  may  obtain  the  relative  cost  of 
footings  plain  and  reinforced.  Thus  at  two  tons  per  sq. 
ft.  earth  pressure,  by  eq.  (i)  h  =.  .7  p  (reinforced)  and 
by  eq.  (7),  h  =  1.4  p  (plain).  By  comparing  the  cost  of 
the  steel  reinforcement  with  that  of  the  additional  excava- 
tion and  concrete  the  relative  costs  of  the  plain  and  rein- 
forced footings  may  be  found. 


DESIGN  OF  COLUMNS.— In  the  design  of  concrete 
columns  reinforced  with  steel  it  is  essential  to  keep  in 
mind  the  rational  use  of  steel  as  a  reinforcement  in  con- 
crete, namely,  to  take  tensile  stresses.  When  a  prism  is 
compressed  longitudinally,  its  diameter  is  increased,  hence 
the  outer  fibers  are  put  under  annular  tension.  Hoops  or 
211 


spirals  bedded  near  the  surface  of  a  circular  column  will 
[  resist  this  tension  and  relieve  the  concrete.  Hoops  would 
have  to  be  welded  into  solid  rings  to  be  of  use,  but  a  spiral 
•may  be  used  in  long  lengths.  M.  Considere  in  a  series 
of  tests  on  hooped  concrete  columns  found  that  they  ex- 
hibited great  strength  against  compressive  loads.  They 
also  showed  regularity  in  the  matter  of  failure.  Where 
a  plain  concrete  column  would  break  suddenly  without 
warning,  a  hooped  column  would  hold  together  after  cracks 
had  shown  partial  failure  to  have  occurred.  These  are 
desirable  qualities  in  any  kind  of  construction.  Columns 
reinforced  with  longitudinal  rods  only  did  not  show  much, 
if  any,  advantage  over  plain  columns.  Longitudinal  rods, 
however,  are  very  useful  in  connection  with  a  coil  to 
space  the  loops  and  to  tie  the  concrete  together  longi- 
tudinally, also  to  assist  in  resisting  flexure  in  the  column 
due  to  eccentric  or  horizontal  loads. 

It  may  be  shown  by  a  little  computation  that  the  area 
of  metal  required  at  a  given  unit  stress  to  contain  the  liquid 
contents  of  a  cylinder  by  resisting  the  bursting  pressure  is 
double  that  required  to  support  the  same  load  if  the 
cylinder  acts  as  a  column.  M.  Considere  found  by  the 
formulas  for  earth  pressures  that  a  shell  filled  with  sand 
is  2.4  times  as  effective  to  sustain  the  load  as  it  would  be 
in  the  form  of  a  column,  at  the  same  unit  stress,  and  his 
experiments  along  that  line  confirm  his  calculations.  This 

would  mean  that  the  lateral  pressure  of  the  sand  is      • 

4.  o 

times    its    longitudinal   pressure.     If,   then   we   treat   the 
disintegrated   concrete,   at   failure,   as   a   substance   whose 

pressure  against  the  spirals  is  -~   times  that  of  a  liquid 

confined  in  a  cylinder,  we  may  arrive  at  the  tension  on  a 
spiral.  In  the  tests  above  referred  to  some  very  high  unit 
loads  were  shown  at  failure,  while  some  of  the  tests 
failed  between  two  and  three  thousand  pounds  per  square 
inch.  While  the  hoops  or  coils  may  hold  the  disintegrated 
concrete  together  and  show  high  unit  loads  before  ulti- 
212 


mate  failure,  the  nature  of  the  material  as  commercially 
made  does  not  justify  a  higher  safe  unit  load  than  about 
550  Ibs.  per  sq.  in.  The  concrete  between  the  spirals  is 
in  no  better  shape  to  resist  compression  than  that  in  a 
beam.  Using  this  unit  load  in  short  columns  (under  ten 
diameters  in  length)  we  have  for  our  effective  liquid 
pressure  550  -f-  4.8  =115  Ibs.  per  sq.  in. 

Let  D  =  outside  diameter  of  column  and  1/%D  =  pitch 
of  coil,  in  inches. 

The  tension  on  a  coil  = 

• 

115X— X—  D=7.2D2. 

2        8 

Allowing  12,500  Ibs.  per  sq.  in.  on  the  steel  we  have  for 
square  rods  of  diameter  d  inches 

12,500  d2  =  7.2  D2. 

Or,  d~~]&D  nearly- 

If  the  diameter  of  coil  be  made  ^  that  of  the  column 
and  that  of  the  steel  be  made  1-40  of  the  same  the  stress 
on  steel  will  be  practically  12,500  Ibs.  per  sq.  in. 

It  is  recommended  that  round  or  octagonal  columns  be 
used  and  that  the  full  area  of  the  circle  be  included  as 
taking  the  load,  also  that  square  rods  be  used  having  a 
diameter  one-fortieth  that  of  the  column  in  a  coil  with  a 
pitch  one-eighth  that  of  the  column.  Where  1-40  D  would 
give  an  odd  figure  the  nearest  sixteenth  or  eighth  may  be 
used  and  the  pitch  made  five  times  as  great. 

In  proportioning  the  longitudinal  rods  we  may,  in  order 
to  establish  a  rule  for  their  size,  follow  the  method  em- 
ployed by  Marsh  in  "Reinforced  Concrete"  and  allow 
them  to  take  the  outward  force  of  the  concrete  between 
the  spirals.  If  we  assume  eight  square  rods  placed  verti- 
cally inside  of  the  coil,  their  clear  span  is 

lT~""4lT~~~T(f' 

The  outward  force  from  the  115  Ibs.  per  sq.  in.  of  assumed 
218 


liquid  pressure  is  115  X       r       D  -+-  8  per  inch.     Being 
fixed  ended  their  moment  is 


UoXx. 

Equating  this  to  12,500  d'z  -f-  6,  the  resisting  moment  of 
square  rods  of  a  diameter  d\  we  obtain 

d<=^. 

38 

This  is  close  to  one-fortieth  of  the  column  diameter; 
ice  eight  rods  of  the  same  diameter  as  that  used  in 

le  coil  may  be  placed  on  the  inside  of  the  coil  and  wired 
to  the  same.  Where  a  coil  ends  the  next  should  lap  not 
less  than  half  a  coil,  which  would  be  about  55  diameters. 

For  columns  more  than  ten  diameters  in  length  it  is 
recommended  that  smaller  unit  loads  be  used,  down  to  a 
minimum  of  370  Ibs.  per  sq.  in.  at  25  diameters.  They 
should  not  be  any  more  slender  than  one-twenty-fifth  of 
the  length.  Between  10  and  25  diameters  the  allowed  unit 
pressure  would  be  found  by  the  following  formula: 

/>=670-12  -^ 

where  p  —  pressure  per  square  inch, 
/  =  length  in  inches, 

D  =  diameter  in  inches. 

It  is  recommended  that  the  same  reinforcement  be  used 
in  all  columns  of  a  given  diameter,  so  that  flexure  will 
be  taken  care  of  in  long  columns. 


THE  DESIGN  OF  CONCRETE  STEEL  BEAMS  AND 
SLABS 

Sir:  Referring  to  the  papers  by  Mr.  Edward  Godfrey, 
published  in  your  issues  of  March  15  and  July  12,  I  con- 
tend that  the  formulas  and  rules  given  by  Mr.  Godfrey 
are  not  sanctioned  by  practice. 

Tests  have  shown  that  the  adhesion  between  steel  and 
concrete  decreases  with  the  diameter  of  the  rods  embedded 


(Service  Francais  des  Phares  et  Balises,  etc),  and  fol- 
lowing the  rules  given  by  Mr.  Godfrey,  to  use  rods  of  a 
diameter  no  more  than  1-200  of  the  span  of  the  beam,  the 
designer  will,  in  many  cases,  get  too  small  rods.  For| 
example,  for  a  beam  of  a  span  of  6  ft.  the  rods  are  to  bej 


.. 

A  good  designer  will  never  use  M-in.  rods  in  a  beam. 
Rods  for  beams  especially  should  have  sufficient  stiffness 
not  to  bend  at  many  points  under  the  load  of  the  concrete. 
If  too  small  rods  are  used  it  will  be  very  difficult  to  assure 
their  distance  from  the  bottom.  To  choose  the  proper  diam- 
eter of  the  rods  in  each  case  the  designer  should  have  had 
practical  experience;  otherwise  he  may  sometimes  choose 
rods  not  easy  to  handle  and  which  will  not  always  allow 
him  to  get  into  the  work  the  reinforcement  made  with  a 
pencil  on  drawing  paper  in  the  office. 

As  for  the  space  between  the  rods,  the  rule  given  by  Mr. 
Godfrey  will  induce  the  designer  to  use  too  large  beams. 
In  such  beams  longitudinal  cracks  occur  between  the  rods. 

Stirrups  are  very  useful  and  increase  the  strength  of  the 
beam.  Well  designed  beams  reinforced  with  stirrups  will 
not  fail  as  shown  by  Mr.  Godfrey  on  the  sketch  on  page 
30  of  Engineering  News  of  July  12,  though  the  height 
be  greater  than  i-io  of  the  span,  and  by  the  by,  I  would 
ask  Mr.  Godfrey  why,  in  the  example  given  by  him  (Eng. 
News,  March  15),  he  does  not  follow  his  own  theory, 
assuming  for  the  main  girder  of  a  span  of  20  ft.  a  depth 
of  32  ins.  instead  of  i-io  X  240  =  24  ins.  As  for  the 
economy  of  beams  designed  according  to  the  rules  given 
by  Mr.  Godfrey  it  seems  to  me  to  be  very  problematical. 
A  steel  area  of  i%  per  cent  may  be,  when  the  depth  and 
width  of  the  beam  are  increased  beyond  certain  limits, 
too  expensive  for  the  purpose.  To  get  a  good  idea  about 
the  cost  of  reinforced  beams  I  would  suggest  that  the 
211 


weight  of  the  steel  be  given  in  pounds  and  the  amount  of 
concrete  in  cu.  ft.    Very  truly  yours, 

Michael  Morssen. 
38  West  26th  St.,  New  York  City,  July  15,  1906. 


THE  DESIGN  OF  REINFORCED  CONCRETE  BEAMS 

AND  THE  LOCATION  OF  MAXIMUM 

MOMENT  IN  A  FOOTING 

Sir:  The  writer  has  followed  with  much  interest  the 
development  of  a  theory  of  reinforced  concrete  design  as 
i  presented  by  Mr.  Edward  Godfrey,  and  the  various  com- 
I  ments  and  criticisms  thereon  by  other  engineers.  That 
this  is  the  writer's  first  participation  in  the  discussion 
is  due  to  the  fact  that  he  disagrees  so  entirely  with  Mr. 
Godfrey's  fundamental  assumptions  that  there  is  no  pos- 
sibility of  carrying  on  a  reasonable  controversy.  As 
stated  in  the  columns  of  this  paper,  and  elsewhere,  the 
writer  believes  that  reinforced  concrete  should  be  designed 
for  the  actual  loads  to  be  carried,  the  factor  of  safety 
being  obtained  by  assigning  allowable  working  stresses 
to  the  concrete  and  steel  respectively.  Where  the  distance 
of  the  neutral  axis  from  the  compression  surface  of  a 
beam  or  slab  is  introduced  in  a  formula,  the  value  used, 
in  the  writer's  opinion,  should  be  that  which  exists  under 
the  working  load,  when  the  unit  stresses  in  concrete  and 
steel  do  not  exceed  their  allowable  limits.  All  authorities 
seem  to  agree  that,  even  for  the  same  beam  or  slab,  the 
neutral  axis  is  in  an  entirely  different  position  under 
the  breaking  load.  Without  going  into  the  question  of 
formulas  at  all,  there  would  seem  to  be  no  reason  why 
reinforced  concrete  should  not  be  subjected  to  the  same 
rules  as  those  which  govern  designing  in  other  materials. 
These  require  the  stresses  under  actual  working  load  to 
be  determinate,  and  that  they  shall  not  exceed  the  allow- 
able values  prescribed  for  each  kind  of  material.  No 
design  that  has  not  been  made  on  this  basis  can  comply 

216 


with  building  laws,  architects'  specifications,  and  the  like, 
which  almost  invariably  express  their  requirements  in  the 
form  of  allowable  working  stresses.  It  should  be  apparent 
that  no  one  formula,  involving  such  variable  quantities  as 
the  coefficient  of  elasticity  for  concrete  in  compression,  and 
the  distance  of  neutral  axis  from  compression  surface,  can 
or  should  be  used  for  both  ultimate  and  working  loads. 
Let  us  say,  for  example,  that  a  beam  has  been  designed 
by  such  a  formula  to  fail  at  four  times  the  working  load, 
and  that  the  maximum  compression  in  concrete  at  the 
breaking  load  is  2,000  Ibs.  per  sq.  in.  Does  anyone  sup- 
pose that  under  the  working  load  the  maximum 
compression  in  the  concrete  is  necessarily  one-fourth 
of  2,000,  or  500  Ibs.  per  sq.  in.?  It  may  be 
more  or  less,  according  to  circumstances,  and  yet  how 
few  adherents  of  this  method  re-compute  their  designs 
to  ascertain  the  actual  maximum  working  stresses,  and  to 
make  sure  they  do  not  exceed  the  law  or  the  specifications. 
Many  would  not  know  how  to  re-compute  them,  since 
their  favorite  formula  would  have  to  be  altered  by  the 
substitution  of  a  new,  and  higher,  elastic  coefficient  for 
concrete,  and  a  new,  and  greater,  distance  of  the  neutral 
axis  from  the  compression  surface. 

In  regard  to  the  percentage  of  steel  to  be  used,  the  writer 
has  always  maintained  that  this  is  a  question  not  only 
of  structural  efficiency,  but  also  of  economy  of  cost  and 
architectural  restrictions  and  requirements.  We  know  that 
in  every  member  subjected  to  pure  transverse  bending,  the 
total  compressive  stress  on  one  side  of  the  neutral  axis 
must  equal  the  total  tensile  stress  on  the  other  side.  (Re- 
markable as  it  may  seem,  the  writer  has  heard  this  well- 
known  fact  denied  by  men  in  very  responsible  positions.) 
There  must,  therefore,  be  a  certain  ratio  of  steel  area  in 
tension  to  concrete  area  in  compression  (neglecting  the 
concrete  in  tension)  which  under  working  loads  will  give 
the  maximum  allowable  intensities  of  stress  in  each  ma- 
terial. This  is  the  structurally  economic  ratio.  If  a 
greater  percentage  of  steel  be  used,  the  maximum  allowable 
217 


intensity  of  compressive  stress  in  the  concrete  becomes  the 
factor  which  fixes  the  resisting  moment,  and  hence  the 
working  load.  Under  this  same  load,  the  intensity  of 
tensile  stress  in  the  steel  will  not  attain  its  allowable 
maximum  working  value,  and  the  design  will  be  structur- 
ally uneconomic.  But  for  easily  conceivable  reasons  the 
price  of  concrete  may  be  very  high,  and  that  of  steel  very 
low,  or  again,  architectural  peculiarities  may  have  limited 
the  size  or  shape  of  the  beam  or  slab.  Under  such  con- 
ditions, the  higher  percentage  of  steel  may  give  the  great- 
est economy  of  cost,  and  the  man  who  clings  to  a  hard 
and  fast  percentage  throughout  his  designing  will  be  at  a 
serious  disadvantage. 

The  writer  believes  that  concrete  engineers  will  be  almost 
unanimous  in  opposing  Mr.  Godfrey's  statement  that  the 
slab,  for  a  certain  width  on  each  side  of  the  beam  at  any 
rate,  should  not  be  considered  as  part  of  the  compression 
flange  of  the  beam,  if  the  concrete  is  deposited  simul- 
taneously and  shearing  stresses  provided  for  in  the  design. 
The  analogy,  submitted  by  Mr.  Godfrey  in  your  issue  of 
July  12,  of  a  buckle  plate  in  a  steel  floor  does  not  seem 
to  fit  the  case.  If  we  may  consider  the  table  of  a  steel 
T-beam,  whose  width  is  generally  more  than  ten  times 
the  thickness  of  the  stem,  as  part  of  the  beam,  it  would 
not  seem  unreasonable  to  consider  a  width  of  slab  equal 
to  ten  times  the  width  of  the  concrete  beam,  as  an  integral 
part  of  such  beam. 

From  the  foregoing  remarks,  it  should  be  evident  that 
the  writer  must  forbear  discussing  Mr.  Godfrey's  mathe- 
matical deductions,  since  there  is  so  great  a  difference  of 
opinion  at  the  very  start.  One  point  will  be  mentioned 
in  regard  to  footing  design.  It  is  the  writer's  belief  that 
where  a  cap  stone  or  column  base  is  superimposed  on  a 
footing  slab,  the  maximum  bending  moment  in  the  slab 
occurs  at  the  center.  To  compute  the  slab  as  a  cantilever 
whose  length  equals  the  projection  beyond  the  cap  stone, 
requires  that  the  cap  stone  itself  should  be  strong  enough 
to  take  at  its  extreme  edge  the  entire  upward  pressure  on 
218 


the  projection.  As  such  is  seldom  the  case,  the  writer  be- 
lieves in  using  the  old  reliable  formula: 

M=JL(l-a) 

for  the  bending  moment  at  the  center  of  the  footing,  P 
being  the  column  load,  /  the  length  of  footing  and  a  the 
length  of  cap  stone  or  column  base.  The  reinforcing  bars 
are  arranged  exactly  as  a  grillage  of  iron  beams  would 
be,  the  strips  running  perpendicular  to  each  other.  In 
fact,  a  reinforced  footing  may  be  economically  designed 
in  practically  the  same  manner  as  an  I-beam  grillage,  the 
only  difference  being  that  the  successive  tiers  are  all  in 
the  same  plane  instead  of  being  superimposed  one  above 
the  other. 

Before  closing  this  letter,  the  writer  wishes  to  acknowl- 
edge the  fact  that  it  does  not  refute  Mr.  Godfrey's  theories. 
As  previously  stated,  it  is  impossible  to  debate  the  matter 
from  two  such  entirely  different  points  of  view,  and  like 
the  closing  addresses  of  two  opposing  lawyers  before  a 
jury,  these  letters  mean  but  little  until  the  verdict  is 
rendered  by  the  readers  of  Engineering  News.  Respect- 
fully yours, 

John  Hawkesworth. 

loo  W.  Both  St.,  New  York,  July  27,  1906. 

•    . 

Sir:  I  beg  to  thank  you  for  the  opportunity  to  reply 
to  the  letters  of  Mr.  Michael  Morssen  and  Mr.  John 
Hawkesworth.  ? 

Mr.  Morssen  says  that  the  formulas  and  rules  given 
by  me  are  not  sanctioned  by  practice.  My  purpose  in 
writing  was  largely  to  show1  that  these  rules  in  particular 
are  overlooked  in  practice.  Theory  and  practice  must  go 
hand  in  hand;  each  needs  correction  from  the  other.  No 
system  of  construction  was  ever  perfected  by  theory  alone, 
and  none  was  every  perfected  by  practice  alone.  Practice 
has  made  many  test-beams  with  short  thick  rods,  and 
these  rods  pull  out  of  the  concrete  just  as  theory,  or  the 
219 


rule  given  by  me,  would  predict.  This  kind  oi  practice 
is  wasting  steel  that  cannot  develop  its  strength.  Practice, 
of  a  construction  in  its  infancy,  is  not  a  competent  witness, 
where  alleged  improvements  on  itself  are  concerned.  . 

Mr.  Morssen  makes  an  indefinite  assertion  to  the  effect 
that  the  adhesion  between  steel  and  concrete  decreases 
with  the  diameter  of  the  rods  embedded,  and  he  cites 
French  authority  to  back  his  statements,  to  which  I  have 
not  access.  No  one  will  deny  that  the  adhesion  decreases 
with  the  diameter  of  the  rods  embedded.  The  tensile 
strength  of  the  rods  decreases  with  the  square  of  the 
diameter  of  the  rod  embedded.  Will  Mr.  Morssen  assert 
that  one  rod  i-in.  square  and  embedded  12^/2  ins.  in  con- 
crete will  hold  with  greater  force  than  sixteen  separate 
rods  54-in-  square  embedded  the  same  distance?  The 
common  standard  of  adhesion  or  grip  of  plain  rods  is 
the  amount  of  area  in  contact  with  the  concrete,  and  a 
simple  calculation  will  show  that  rods  of  different 
diameters,  in  order  to  have  the  area  in  contact  in  propor- 
tion to  their  tensile  strength  will  be  embedded  a  given 
number  of  diameters.  While  it  is  admitted  that  the  unit 
value  of  the  adhesion  is  variable,  as  the  other  qualities  of 
concrete  are  also  variable,  it  is  generally  considered  that 
a  rod  embedded  50  diameters  in  concrete  will  develop  its 
full  strength,  or  at  least  its  elastic  limit,  if  the  rod  be 
surrounded  with  a  thickness  of  concrete  equal  to  several 
times  its  diameter,  the  concrete  having  set  in  the  air. 

Mr.  Morssen  gives  an  example  of  a  "beam"  of  6-ft.  span. 
If  the  span  were  only  6  ft.,  would  not  a  slab  be  in  order? 
He  says  a  good  designer  will  never  use  3^-in.  rods  in  a 
beam.  As  I  have  used  2i-in.  rods  in  the  design  of  a  slab 
I  will  refrain  from  answering  this. 

I  have  no  apology  to  make  for  the  contention  that  the 
proper  design  of  reinforced  concrete  demands  that  the 
steel  be  well  distributed  and  of  comparatively  small  diame- 
ter, rather  than  being  concentrated  in  elements  of  large 
diameter. 

Mr.  Morssen  says  that  the  rule  given  by  me  will  induce 
220 


the  designer  to  use  too  large  beams,  and  that  in  such 
beams  longitudinal  cracks  occur  between  the  rods.  Can 
he  cite  any  experience  or  results  of  tests  to  substantiate 
this? 

Another  dogmatic  assertion  of  Mr.  Morssen' s  is  that 
well-designed  beams  reinforced  with  stirrups  will  not  fail 
as  shown  by  me  though  the  height  be  greater  than  one- 
tenth  of  the  span.  I  made  tests  on  quite  a  number  of 
beams  with  stirrups  in  a  finished  building.  The  principal 
mode  of  failure  was  just  as  my  sketch  shows.  In  Pro- 
ceedings of  the  American  Society  for  Testing  Materials, 
Vol.  IV,  p.  498,  Prof.  F.  E.  Turneaure  describes  some  test- 
beams  which  were  6x6  ins.  and  60  ins.  in  span,  rein- 
forced with  stirrups,  spaced  3  ins.  apart.  On  page  507 
Prof.  Turneaure  says:  "In  but  a  few  cases  was  the 
failure  free  from  the  influence  of  shearing  stresses,  the 
rupture  usually  occuring  outside  of  the  load  and  on  a 
diagonal  line."  These  beams  were  one-tenth  of  the  span 
in  height,  and  they  had  stirrups,  and  they  failed  about  as 
my  sketch  shows. 

The  reason  I  did  not  "follow  my  own  theory,"  as  Mr. 
Morssen  puts  it  in  the  girder  of  2O-ft.  span  is  because  it 
would  give  a  clumsy  beam  to  make  its  depth  one-tenth  of 
the  span.  Further,  I  wanted  to  give  an  example  of  a 
beam  reinforced  partially  with  rods  curved  up  and  anchored 
for  their  full  stress  at  the  ends,  another  part  of  the  theory. 

Mr.  Morssen  says  that  a  steel  area  of  i^J  per  cent  may 
be  too  expensive  for  the  purpose.  Is  it  too  much  or  too 
little?  (requiring  too  much  concrete).  I  have  been  criti- 
cised on  the  ground  that  it  is  too  much  from  alleged 
theoretical  considerations.  If  Mr.  Morssen  will  look  up 
practice  as  it  is  exhibited  in  descriptions  of  reinforced 
concrete  construction  in  the  engineering  papers,  I  think 
he  will  find  that  leaving  out  the  area  of  the  slab,  as  having 
no  place  in  the  beam,  2  or  3  per  cent  of  steel  is  not 
uncommon. 

It  is  a  pleasure  to  reply  to  a  letter  in  the  tone  of  that 


of  Mr.  John  Hawkesworth,  which  you  have  kindly  sub- 
mitted to  me.  This  letter  is  from  one  who  is  manifestly 
a  fellow  seeker  after  the  truth.  A  letter  in  a  very  dif- 
ferent tone  came  to  me  recently,  touching  on  some  of 
the  same  points  mentioned  in  this  one,  from  one  who 
has  not  the  temerity  to  express  publicly  the  final  judg- 
ment which  he  snapped  on  my  theory  and  deductions. 

The  question  of  using  a  certain  unit  stress  on  the  steel 
and  concrete  and  proportioning  the  beam  on  that  basis, 
or  of  using  certain  ultimate  values  and  then  allowing 
as  a  safe  load  some  fraction  of  the  ultimate  capacity  is 
too  extensive  to  be  discussed  here  as  a  general  question. 
When  confined  to  a  single  case,  as  reinforced  concrete,  it 
is  merely  a  question  of  means;  identical  results  may  be 
obtained  by  either  means. 

In  reinforced  concrete  design  it  is  convenient  to  use  a 
certain  factor  of  safety  based  on  the  ultimate  strength 
of  the  parts  because  of  the  dissimilar  materials  dealt  with 
and  the  desirability  of  having  the  same  relative  strength 
in  each.  In  choosing  an  ultimate  value  for  the  steel  I 
did  not  lose  sight  of  the  actual  amount  of  the  safe  value. 
This  is  made  clear  by  my  first  paper  on  the  subject  (Engi- 
neering News,  March  15,  1906),  for  I  there  criticise  the 
use  of  high  elastic  limit  steel,  because  the  resultant  safe 
load  on  the  steel  when  the  factor  of  safety  is  applied  is 
too  great.  Where  is  the  difference  between  using  10,000 
Ibs.  per  sq.  in.  on  the  steel  and  500  Ibs.  per  sq.  in.  on  the 
concrete  and  using  40,000  Ibs.  per  sq.  in.  on  the  steel 
and  2,000  Ibs.  on  the  concrete  with  a  factor  of  safety  of 
four  ? 

On  the  location  of  the  neutral  axis  of  a  beam  or  slab 
I  have  said  something  before  in  these  columns.  The  case 
is  one  that  has  entirely  too  many  complications  to  be  settled 
by  theory  with  no  other  data  than  the  relative  moduli  of 
elasticity  of  steel  and  concrete.  The  shrinking  of  con- 
crete in  setting  is  one  of  the  complications.  The  tensile 
strength  of  the  concrete  is  another.  Measurements  to 
locate  the  neutral  axis  of  beams  under  test  have  shown 
222 


that  it  is  close  to  the  middle  of  the  depth  of  the  concrete 
beam  under  safe  loads.  I  have  taken  it  at  the  middle  in  all 
of  my  formulas.  Now  taking  the  neutral  axis  in  the  center 
of  depth  of  beam  and  assuming  that  the  intensity  of  stress 
in  concrete  varies  uniformly  from  the  neutral  axis  up, 
there  remains  but  one  factor  to  fix  the  percentage  of  steel, 
namely,  the  relative  unit  stress  on  concrete  and  steel. 
If  this  is  as  I  to  20  the  percentage  must  be  iJ4-  This  is 
very  simply  found  by  the  principle  which  Mr.  Hawkes- 
worth  states  and  which  I  have  given  in  both  of  my  papers, 
namely,  that  the  amounts  of  stress  in  steel  and  concrete 
must  be  equal.  Any  greater  percentage  of  steel  in  a 
rectangular  beam  means  a  greater  stress,  relatively,  on  the 
concrete.  Any  less  means  a  greater  relative  stress  on  the 
steel. 

As  to  the  floor  slab  acting  as  a  T-beam:  It  would  of 
course  be  allowable  to  use  a  part  of  the  floor  slab,  pro- 
vided it  was  placed  at  the  same  time  as  the  beam,  and 
provided  the  owner  were  forbidden  to  cut  holes  in  the 
slab,  as  he  might  think  he  had  a  right  to  do.  However, 
the  T-beam  method  can  only  show  to  its  credit  a  saving 
of  concrete  around  the  reinforcing  rods,  just  where  the 
concrete  is  needed  to  protect  and  grip  the  steel  and  to 
transfer  the  shear.  I  tested  some  beams  in  a  building 
that  were  3  ins.  wide  and  were  reinforced  with  i^-in. 
square  rods.  Is  this  enough  concrete  to  protect  and  grip 
a  rod  of  this  size  or  to  take  the  horizontal  shear?  My 
tests  conclusively  proved  otherwise. 

Mr.  Hawkesworth  criticises  my  mathematical  deductions 
on  the  wall  footing,  and  states  that  where  a  cap  stone  or 
a  column-base  is  superimposed  on  a  footing  slab,  the 
maximum  moment  in  the  slab  occurs  at  the  center.  A 
reinforced  concrete  footing  would  probably  be  surmounted 
by  a  concrete  wall  put  in  at  the  same  time,  and  a  column 
base  would  probably  have  a  plinth  of  concrete  Upon  which 
it  rests,  instead  of  being  placed  directly  on  the  slab.  In 
these  cases  the  depth  of  beam  would  be  augmented  and 
the  tension  on  steel  diminished  toward  the  center. 


Mr.  Hawkesworth  gives  an  "old  reliable"  formula  for 
the  bending  moment  at  the  center  of  a  footing.  It  is 
presumed  that  he  does  not  mean  that  this  formula  ex- 
presses the  bending  moment  at  the  center  of  a  column,  as 
this  center  is  a  vertical  line  and  can  have  no  section 
modulus.  And  yet  this  is  what  his  reasoning  seems  to 
lead  to.  This  is  a  formula  for  the  bending  moment  in  a 
row  of  I-beams  in  a  grillage,  at  the  center  plane  of  the 
column  or  wall 


Beams  A  in  the  accompanying  sketch,  at  (a),  could  be 
proportioned  by  this  formula.  Beams  B  could  also  be 
proportioned  by  the  same.  If,  however,  the  latter  spread 
out  to  the  full  width  of  the  footing,  those  outside  of  the 
column  base  would  be  absolutely  useless.  There  is  no 
analogy  between  these  steel  grillage  beams  and  the  rein- 
forcing bars  as  shown  at  (b).  (I  assume  this  is  the 
manner  of  reinforcing  referred  to  by  Mr.  Hawkesworth. 
My  timid  critic  says  this  is  the  common  way  of  placing 
the  rods.)  It  is  not  even  approximately  correct  to  use  the 
so-called  old  reliable  formula.  By  that  formula  each  set 
of  beams  takes  the  entire  reaction  and  transmits  it  to 
the  set  above.  If  we  assume  that  rods  A  in  the  reinforced 
concrete  footing  take  all  of  the  reaction,  we  must  also 
assume  that  they  give  that  reaction  to  such  of  rods  B  as 
lie  under  the  column  base.  But  this  puts  excessive  load 
on  those  few  rods,  and  leaves  idle  the  rods  B  not  under 
the  column  base.  On  the  assumption  that  both  sets  of 
rods  act  together,  necessarily  more  of  the  load  must  be 
taken  by  the  rods  lying  under  the  base,  and  the  formula  is 
seen  to  be  inapplicable. 

224 


By  the  use  of  diagonal  rods  the  upward  force  on  the 
footing  at  any  part  of  the  same  is  carried  directly  to  the 
base  by  the  shortest  route.  Each  part  is  taken  care  of, 
and  there  is  some  excess  of  strength  at  the  sides  by 
reason  of  the  additional  depth  used  in  column  bases  over 
wall  footings. 

The  formula  given  by  Mr.  Hawkesworth,  as  applied  to  a 
wall,  is  based  on  the  assumption  that  the  wall  load  is  per- 
fectly uniform  on  the  slab.  This  would  be  true  if  the 
wall  were  a  fluid  or  yielding  body  that  would  take  the 
shape  of  the  deflecting  footing.  But  when  the  footing  de- 
flects, the  tendency  is  to  throw  the  load  close  to  the  edge 
diminishing  the  bending  moment.  For  all  ordinary  earth 
pressures  the  depth  of  footing  is  a  large  fraction  of  the 
projection  beyond  the  wall.  A  considerable  part  of  this 
projection  could  be  made  in  a  plain  concrete  footing  as- 
suming a  low  modulus  of  transverse  strength.  It  is  legiti- 
mate to  make  use  of  this  surplus  strength  of  the  con- 
crete to  balance  the  small  increase  in  the  moment  within 
the  edge  of  the  wall,  which  an  only  partially  correct  theory 
finds  to  exist.  Yours  very  truly, 

Edward  Godfrey. 

Monongahela  Bank  Bldg.,  Pittsburg,  Pa.,  Aug.  10,  1906. 


THE     DESIGN     OF     REINFORCED     BEAMS     AND 
SLABS 

Sir :  I  beg  once  more  to  use  the  columns  of  your  paper 
to  reply  to  the  long  and  interesting  letter  of  Mr.  Godfrey, 
published  in  your  issue  of  August  23.  In  this  letter  Mr. 
Godfrey  repeats  good  and  useful  principles  well  known 
by  all  proper  designers  in  reinforced  concrete  as  well  as 
by  the  writer.  It  is  very  old  matter  that  theory  and 
practice  must  go  hand  in  hand,  that  rods  for  reinforce- 
ment should  be  embedded  a  given  number  of  diameters 
to  develop  their  full  strength  and  that  the  proper  design 
of  a  slab  and  beam  demands  that  the  steel  be  well  dis- 
225 


tributed  and  in  small  rods  rather  than  being  concentrated 
in  elements  of  large  diameters.  But  repeating  these  prin- 
ciples Mr.  Godfrey  does  not  say  that  he  maintains  again 
his  rules  in  their  full  conclusion  as  they  are  printed  in 
your  issues  and  with  which  the  writer  does  not  agree. 
These  principles  are  (issue  of  March  15,  pp.  291,  292)  : 

(1)  The  rod  should  be  no  more  than  1-200  of  the  span. 

(2)  The   maximum   depth   of  a  beam   is   20  times   the 
diameter  of  the  rod  embedded  or  i-io  of  the  span.     The 
maximum  depth  should  be  used  only  in  extreme  cases. 

In  your  issue  of  July  12,  p.  30,  Mr.  Godfrey  says  that 
by  his  rules  it  becomes  a  simple  matter  to  design  beams 
and  slabs  in  this  comparatively  new  combination  of  ma- 
terial, which  is  to  say  that  design  will  be  much  easier 
than  it  was  till  now.  This  is  not  the  writer's  belief.  The 
examples  given  by  the  writer  in  his  first  letter  (August 
2)  were  only  to  show  to  what  design  these  rules  may 
lead  if  the  designer  follow  them  literally.  Good  designers 
who  know  their  business  will  in  the  most  cases  not  fol- 
low these  rules  as  their  own  author  has  done  in  his  ex- 
ample cited.  For  poor  designers  who  overlook  the  funda- 
mental principles  stated  above  and  who  do  not  know  much 
about  reinforced  concrete,  rules  as  these  given  by  Mr. 
Godfrey  become  a  danger  and  make  them  advance  from 
bad  to  worse.  Just  because,  as  says  Mr.  Godfrey  himself, 
this  kind  of  construction  is  in  its  infancy,  the  writer's 
belief  is  that  it  will  be  a  guess  matter  to  give  now  rules 
to  govern  the  proper  proportioning  of  the  steel  and  the 
limiting  length  of  the  span,  etc.  Nevertheless,  papers  as 
these  of  Mr.  Godfrey  and  very  useful  and  interesting. 

One  point  which  seems  to  me  to  be  overlooked  by  Mr. 
Godfrey  is  the  fact  that  reinforced  slabs  and  beams  are 
in  the  most  cases  designed  as  continuous  elements  and 
the  rods  of  one  slab  or  beam  overlap  the  rods  of  the 
next,  and  then  the  length  of  the  rod  embedded  in  con- 
crete exceeds  in  many  cases  the  length  required  by  the 
calculation  though  the  diameter  be  larger  than  1-200  of 
the  span. 

226 


Mr.  Godfrey  criticises  the  writer's  example  with  a  beam 
of  a  span  of  6  ft.,  saying  that  a  slab  should  be  in  order 
for  this  span.  I  would  answer  that  beams  at  a  span  of 
6  ft.  or  less  are  often  to  be  designed  over  openings  and 
have  sometimes  to  carry  large  concentrated  loads  which 
a  slab  would  not  do. 

As  to  my  so-called  (by  Mr.  Godfrey)  dogmatic  asser- 
tions about  the  failure  of  well  designed  beams,  overlook- 
ing laboratory  tests  with  small  elements,  I  would  refer 
Mr.  Godfrey  to  the  text-books  of  Christophe,  p.  490 
(French  text)  and  of  Prof.  Morsch,  "Der  Betoneisenbau," 
p.  121,  etc.,  where  the  failure  of  beams  is  discussed,  and 
he  will  see  that  it  is  not  only  my  own  judgment.  The 
finished  building  test  by  Mr.  Godfrey  in  which  beams  have 
failed  by  shear  under  the  test  load  (generally  il/2  to 
2  times  the  live  load  for  which  the  floors  are  designed) 
should  be  of  a  very  poor  design  and  for  this  reason  can- 
not be  cited  as  reference.  The  writer  has  had  the  oppor- 
tunity to  assist  in  tests  made  in  France  (Paris)  and  in 
Germany  (Charlottenburg,  near  Berlin),  and  he  himself 
has  made  many  tests  on  large  elements  and  got  other 
results  than  those  cited  by  Mr.  Godfrey.  The  writer 
believes  that  deep  beams  designed  only  for  the  bending 
moment  will  fail  by  shear  as  well  as  beams  of  a  small 
height  will  do  when  they  have  to  carry  a  concentrated  load 
near  the  support  and  the  reinforcement  was  not  designed 
for  the  purpose. 

To  substantiate  the  assertion  that  in  large  beams  longi- 
tudinal cracks  occur  in  the  spaces  between  the  rods,  the 
writer  would  say  that  an  analogous  fact  occurs  in  slabs 
reinforced  in  one  way  and  to  avoid  these  cracks  additional 
cross-rods  are  embedded.  In  some  large  beams  the  writer 
has  himself  verified  these  cracks  in  cases  in  which  special 
arrangements,  as  little  cross-bars  or  special  U-shaped  stir- 
rups going  under  all  rods  were  not  provided. 

As  to  the  steel  area  to  be  used  the  writer  knows  that 
sometimes  beams  are  designed  with  a  steel  area  of  2  per 
cent  or  more  and  his  idea  was  not  so  much  to  criticise 
227 


this  amount,  as  to  give  a  suggestion  that  when  speaking 
about  the  cost  the  amount  of  concrete  be  given  in  cubic 
feet  and  the  steel  in  pounds  per  lineal  foot  of  beam  or 
per  square  foot  of  slab.  Very  truly  yours, 

M.  Morssen. 

38  West  26th  St.,  New  York,  N.  Y.,  Aug.  26,  1906. 

The  author  did  not  reply  to  the  above  from  Mr.  Morssen. 
Of  course  if  Mr.  Morssen  does  not  elect  to  accept  simplified 
assumptions,  he  does  not  come  in  the  class  to  whom  the 
design  of  reinforced  concrete  beams  is  made  a  simple  mat- 
ter by  those  assumptions.  Mr.  Morssen  begs  the  ques- 
tion in  citing  continuous  beams,  where  the  rod  passes 
into  the  next  beams.  There  are  many  beams  made  that 
are  not  continuous,  and,  in  any  event,  there  must  be  an 
end  to  a  line  of  continuous  beams.  Further,  a  short  beam 
over  a  six-foot  opening  supporting  a  heavy  concentration 
would  probably  be  isolated.  If  such  a  beam  had  thick 
rods  not  positively  anchored  at  the  ends,  it  would  be  faulty, 
and  the  rods  would  pull  out  before  they  received  their 
full  stress,  for  the  simple  reason  that  they  would  not  be 
bedded  deep  enough  in  the  concrete  to  have  the  necessary 
grip. 

It  is  a  far  cry  from  a  slab  not  reinforced  transversely 
to  a  beam  of  width  enough  to  keep  the  steel  reinforcing 
rods  well  separated.  An  isolated  slab  would  not  have 
the  tendency  to  crack  longitudinally  that  there  exists  in 
a  slab  built  in  a  structure.  So  a  beam  of  good  width 
would  not  have  shrinking  forces  on  each  side  of  it  tend- 
ing to  split  it  longitudinally. —  [AUTHOR.] 


CONCERNING  THE  STRESSES  DUE  TO  SHRINK- 
AGE IN  REINFORCED  CONCRETE 

Sir:  In  an  article  in  Engineering  News  of  March  15, 
1906,  on  'The  Design  of  Concrete-Steel  Beams  and  Slabs," 
by  Edward  Godfrey,  he  says  (first  column,  page  291)  : 

The  fact  that  concrete  in  which  steel  is  embedded  has 
228 


been  stretched  out  in  tests  without  cracking  to  elonga- 
tions that  would  rupture  plain  concrete  is  evidence  that 
the  concrete  in  setting  has  shrunk,  thus  putting  the  steel 
under  an  initial  compression  which  must  be  overcome 
before  any  stretch  occurs  in  the  concrete. 

Now  it  seems  to  me  that  when  the  steel  is  put  under 
compression  by  shrinking  of  the  concrete,  the  latter  is  at 
the  same  time  put  under  tension,  and  any  further  load- 
ing of  the  beam  would  all  be  carried  by  the  concrete, 
so  that  it  would  have  to  take  all  the  tension  until  it  has 
stretched  so  far  that  all  the  initial  compression  has  been 
taken  off  the  steel. 

Edwin  Squire. 

Claremont,  California,  July  19,  1906. 

The  author  did  not  make  reply  to  the  above.  He  sees 
the  force  of  Mr.  Squire's  argument.  He  is,  however,  still 
of  the  opinion  that  the  shrinking  of  the  concrete  in  setting 
has  much  to  do  with  its  integrity  under  stress.  The  tests 
which  have  been  heralded  so  widely  in  this  country  as 
disproving  Considered  conclusion,  that  concrete  with  steel 
embedded  will  withstand  cracking  when  the  calculated 
stress  in  the  steel  is  large,  were  made  on  beams  that  were 
kept  in  water  and  thus  prevented  from  shrinking.  (These 
tests  were  made  by  Prof.  Turneaure.  See  Proc.  Am. 
Soc.  for  Testing  Materials,  Vol.  IV.)  It  is  possible  that 
the  concrete,  in  the  beam  which  sets  in  air  and  contracts, 
takes  more  than  its  share  of  the  stress,  so  that  the  tension 
in  the  steel,  and  the  consequent  stretch,  are  not  so  much 
as  calculations  show.  It  is  further  possible  that  between 
a  unit  compression  x  in  a  steel  rod  and  a  unit  tension  y 
the  theory  may  not  hold  in  its  exactness  that  the  dif- 
ference in  length  is  the  same  as  that  which  would  be  pro- 
duced by  a  unit  tension  of  x  plus  3;  on  an  unstressed  rod. 
In  any  event  practice  and  tests  show  that  calculated 
stresses  in  the  steel  in  air  dried  beams  up  to  10  or  12,000 
Ib.  per  sq.  in.  do  not  produce  perceptible  cracks.  Excessive 
shrinking  is,  of  course,  harmful. — [AUTHOR.] 

229 


ON   PROPORTIONING  THE   REINFORCEMENT 
OF  CONCRETE  COLUMNS 

Sir:  In  your  issue  of  July  12,  1906,  Mr.  Edward  God- 
frey treats  at  some  length  the  question  of  design  of  rein- 
forced concrete  columns,  and  develops  formulas  for  pro- 
portioning the  reinforcement  based  upon  the  theory  that 
the  concrete  at  failure  becomes  a  granular  mass,  whose 
lateral  pressure  is  I  divided  by  4.8  times  that  of  a  liquid 
confined  in  a  cylinder.  He  arrives  at  the  conclusion  that 
in  a  circular  column  of  diameter  D  the  spiral  rein- 
forcement should  be  a  square  rod,  whose  side  is  equal  to 
1-40  D,  the  pitch  of  the  coil  equal  to  */6  D,  and  the  longi- 
tudinal reinforcement  8  square  rods  of  the  same  dimen- 
sions as  the  spiral. 

It  seems  to  the  writer  that  your  correspondent  in  his 
fundamental  assumptions  and  deductions  therefrom  has 
been  taking  a  "long  shot." 

The  relation  between  the  lateral  and  the  longitudinal 
pressure  of  a  granular  mass  confined  in  a  cylinder  and 
subjected  to  its  own  weight  or  to  additional  pressure, 
bears  very  little  resemblance  to  that  of  a  fluid  under  sim- 
ilar conditions,  for  the  following  reasons :  In  treating  a 
confined  granular  mass  we  are  dealing  with  a  substance 
in  which  there  is  an  appreciable  friction  between  the 
particles  of  its  own  mass,  as  well  as  a  friction  between 
these  and  the  walls  of  the  confining  cylinder.  This  is 
obvious,  for  one  has  only  to  consider  that  a  bucket  full 
of  sand  thrown  out  upon  a  board  does  not  spread  out  to  a 
uniform  depth,  but  remains  in  a  more  or  less  cone- 
shaped  pile,  neither  will  it  slide  from  the  board  until 
the  latter  is  tilted  to  a  considerable  angle.  Owing  to 
these  physical  facts,  when  a  granular  mass  is  confined  in 
a  cylinder  its  weight  is  supported  partially  by  the  bottom 
of  the  cylinder  and  partially  by  the  sides  acting  as  a 
column,  while  the  sides  are  at  the  same  time  under  ten- 
sion due  to  the  lateral  pressure. 

This   action   of  granular   masses   confined   in   bins,    and 
230 


the  relation  of  lateral  to  longitudinal  pressure,  have  been 
very  thoroughly  investigated  by  Mr.  J.  A.  Jamieson,  of 
Montreal,  and  made  the  subject  of  a  very  complete  paper 
presented  before  the  Canadian  Society  of  Civil  Engineers, 
and  later  published  by  Engineering  News  (March  10, 
1904).  Mr.  Jamieson  found,  for  such  granular  masses 
as  wheat,  corn,  flaxseed,  etc.,  that  when  no  settlement  of 
the  bin  walls  occurred,  approximately  only  20  per  cent  of  the 
confined  mass  was  supported  by  the  bottom  of  the  bin, 
while  the  remaining  80  per  cent  was  supported  by  the  sides 
acting  as  a  column;  that  the  lateral  (maximum)  pressure 
at  any  point  was  practically  constant  and  equal  to  6-10 
of  the  vertical  pressure  when  the  height  of  the  grain 
column  was  equal  to  or  exceeded  about  4  times  the 
diameter  of  the  base;  also  that  it  made  little  or  no  differ- 
ence in  these  relations  if  the  bin  was  round  or  square. 
Among  many  experiments  recorded  by  Mr.  Jamieson  was 
one  on  dry  sand,  and  it  is  interesting  to  note  that  he 
found  approximately  the  same  results  as  for  wheat;  that 
is,  a  ratio  of  lateral  to  vertical  pressure  of  0.65,  and 
81.5  per  cent  of  the  total  weight  carried  by  the  sides  of 
the  bin. 

A  very  simple  experiment  in  line  with  the  above  may 
be  performed  by  making  a  tube,  say  10  ins.  long  and  2 
ins.  in  diameter,  from  thin  writing  paper,  placing  it  on 
end  and  filling  it  with  dry  sand.  When  the  sand  within 
is  subjected  to  pressure,  the  first  noticeable  feature  is  a 
buckling  of  the  walls  of  the  tube,  generally  about  1-3  the 
height  up  from  the  bottom.  Additional  pressure  causes 
rupture,  the  resulting  tear  running  parallel  to  the  long 
axis  of  the  tube.  If  the  length  of  the  tube  be  made  20 
ins.,  the  diameter  remaining  the  same,  and  the  sand  sub- 
jected to  pressure,  there  is  a  buckling  of  the  walls  of  the 
tube  followed  by  a  bending  of  the  whole  and  a  failure 
near  the  center,  the  tear  in  this  case  being  at  right  angles 
to  the  long  axis.  In  the  first  instance  the  walls  acted  as  a 
column  until  they  failed  (buckled),  then  ruptured  under 
a  tensile  stress  such  as  would  be  caused  by  hydraulic 
231 


pressure.  In  the  second  instance  the  walls  failed  by 
buckling,  then  ruptured  under  the  stress  caused  by  the 
bending  moment  at  the  center. 

Sand  confined  in  a  cylinder  can  be  made  to  withstand 
enormous  loads,  limited  only  by  the  strength  of  the  con- 
fining cylinder.  This  is  the  principle  of  sand  wedges  used 
in  arch  construction,  and  is  well  known. 

If  we  are  going  to  treat  the  reinforced  concrete  column 
at  rupture  as  so  much  disintegrated  matter  or  as  sand, 
and  from  this  assumption  develop  formulas  for  ascertain- 
ing the  dimension  of  steel  spirals  to  withstand  this  dis- 
integrating action,  then  there  are  more  and  different  factors 
to  be  considered  than  those  used  by  Mr.  Godfrey.  In 
view  of  Mr.  Jamieson's  experiments,  quoted  above,  the 
lateral  pressure  would  be  0.60  of  the  longitudinal  and 
not  0.21  (i.  e.  I  -f-  4.8)  as  stated  by  your  correspondent. 
That  is,  the  lateral  pressure  is  about  three  times  as 
great  as  he  assumes.  The  matter  of  the  walls  (spirals) 
carrying  80  per  cent  of  the  loading  as  a  column  is  not  taken 
into  consideration  by  him  at  all,  and  it  seems  to  the  writer 
that  it  is  radically  wrong  to  apply  to  a  concrete  column 
this  theory  of  disintegration  which  logically  demands  that 
the  walls  (or  longitudinal  reinforcement)  take  80  per  cent 
of  the  imposed  loading.  To  follow  up  this  line  of  reason- 
ing must  induce  one  to  dispense  with  the  concrete  alto- 
gether and  employ  an  all-steel  column. 

A  mild  steel  rod  in  the  form  of  a  coil  is  metal  not  well 
disposed  to  act  as  a  column  carrying  loads,  and  experi- 
ments on  reinforced  columns  in  which  the  reinforcing 
is  only  spirals  or  hoops  show  a  much  larger  degree  of 
compressibility  under  loading  than  columns  in  which  longi- 
tudinal rods  of  considerable  size  are  employed.  This  is 
well  brought  out  in  Mr.  Howard's  article  in  the  issue 
of  Engineering  News  for  July,  1906,  in  which  he  says, 
"Hooped  columns  are  a  distinct  group  and  decidedly  more 
compressible  than  the  others."  In  the  same  article  it  is 
clearly  shown  that  hooping  a  column  of  1-2-4  concrete 
will  add  greatly  to  its  ultimate  strength,  and  sq  will  the 
232 


addition  of  a  fair  amount  of  longitudinal  metal  (2.86  per 
cent),  while  a  combination  of  the  two  will  further  increase 
the  ultimate  resistance  under  loading.  A  mixture  rich  in 
cement  and  unreinforced  (i  of  cement  to  I  of  sand)  is 
20  per  cent  stronger  than  a  1-2-4  concrete  reinforced  with 
25  hoops  and  4  angles,  and  considerably  more  rigid  under 
loading.  In  these  tests  on  1-2-4  rock  concrete  the  hoops 
were  il/2  ins.  wide  by  */£-in.  (given  as  0.12  in.)  thick 
spaced  at  various  intervals.  The  smallest  recorded  num- 
ber (13)  increased  the  strength  of  the  column  58  per  cent 
above  that  of  the  plain  unreinforced  piece,  while  the  largest 
number  (47)  increased  the  strength  274  per  cent,  raising  it 
to  5,289  Ibs.  per  sq.  in.  In  the  latter  case  the  spacing 
of  the  hoops  was  a  trifle  over  2^  ins.,  or  the  neat  open- 
ing between  the  hoops  was  0.66  times  the  width  of  one 
hoop.  Mr.  Godfrey's  deductions  that  the  diameter  of  the 
square  spiral  rod  should  be  1-40  D,  spaced  l/%  D,  leaves  a 
clear  opening  of  i-io  D  between  the  rods,  which  opening 
is  four  times  the  width  of  the  rod.  This  does  not  look 
like  metal  well  placed  to  confine  a  disintegrating  mass. 

In  a  reinforced  beam  we  place  the  metal  where  it  will 
resist  the  tensile  stresses,  leaving  the  plain,  unreinforced 
concrete  to  take  care  of  the  compressive  stresses  of  500 
ibs.  per  sq.  in.  or  greater.  It  this  is  good  practice  (and 
it  is  a  common  one)  why  should  we  design  a  column  on  a 
basis  of  550  Ibs.  per  sq.  in.  of  compressive  stress  and 
then  reinforce  it.  In  other  words,  unless  we  either  figure 
upon  an  allowable  unit  of  compressive  stress  of  much 
greater  amount  than  550  Ibs.,  or  assume  that  the  longi- 
tudinal reinforcement  carries  a  portion  of  the  imposed 
load,  then  we  have  not  reduced  the  size  of  the  column 
under  that  of  one  not  reinforced,  and  have  added  largely 
to  its  cost.  It  is  the  large  size  of  columns  (compared 
with  steel)  that  in  actual  practice  makes  them  so  objec- 
tionable to  many  architects.  This  size  can  be  reduced  to 
reasonable  limits  by  using  a  concrete  mixture  rich  in 
cement,  reinforced  with  spirals  or  hoops  that  form  a  close 
enclosing  mesh  and  longitudinals  to  whichjthev  are  firmly 

233 


attached,  assigning  to  the  concrete  a  high  compressive 
unit  of  resistance  and  to  the  longitudinals  a  portion  of 
the  imposed  load,  but  not  by  the  formulae  and  method 
suggested  by  your  correspondent.  Very  truly  yours, 

G.  B.  Ashcroft, 
C.  E.  Assoc.  M.  Can.  Soc.  C.  E. 

Supt.  Roman  Stone  Co.,  Ltd. 
Toronto,  Ont.,  Aug.  17,  1906. 


THE  DESIGN  AND  THE  BEHAVIOR  OF  REIN- 
FORCED CONCRETE  COLUMNS 

Sir:  I  have  before  me  proof  of  Mr.  G.  B.  Ashcroft's 
letter  in  which  he  objects  to  my  method  of  proportion- 
ing a  reinforced  concrete  column,  and  thank  you  for 
the  opportunity  to  reply  to  the  same.  The  answers  to 
Mr.  Ashcroft's  objections  are  found  partially  in  the  papers 
which  he  cites 'and  partially  in  his  own  letter. 

I  have  always  considered  the  paper  by  Mr.  J.  A. 
Jamieson  on  tests  on  grain  bins  as  a  very  valuable  con- 
tribution to  engineering  knowledge.  These  tests  were 
made  to  determine  the  relation  between  the  head  of  grain 
in  a  bin  and  the  horizontal  and  vertical  pressures  in  the 
grain,  and  were  not  made  with  a  view  of  finding  the 
bursting  pressure  of  a  confining  cylinder  which  has  no 
longitudinal  strength.  One  experiment  made  by  Mr.  Jamie- 
son  on  a  cloth  cylinder  showed  what  one  naturally  would 
suppose,  namely,  that  if  the  walls  can  yield  vertically  the 
grain  itself  will  support  all  of  the  weight.  In  a  steel 
cylinder  a  large  part  of  the  weight  would  be  carried  by 
the  shell.  A  coil  in  a  reinforced  concrete  column  would 
act  like  the  cloth  cylinder;  that  is,  it  would  take  none 
of  the  load  on  the  column.  Unfortunately  for  column 
investigators,  Mr.  Jamieson  did  not  measure  the  lateral 
pressure  on  the  cloth  cylinder.  However,  among  his  ex- 
periments there  is  one  which  has  a  direct  bearing  on  this 
subject.  The  experiment  referred  to  is  one  in  which  a 
234 


bin  having  sides  that  could  be  raised  and  lowered  was 
filled.  The  pressures  on  the  bottom  and  sides  were 
measured,  and  the  latter  was  found  to  be  about  six-tenths 
of  the  former,  as  stated  by  Mr.  Ashcroft.  Upon  lowering 
the  sides  all  of  the  grain  as  well  as  the  sides  themselves 
was  supported  on  the  bottom.  Mr.  Jamieson  says  (Eng. 
News,  March  10,  1904,  p.  238)  : 

"On  the  bin  being  again  lowered  to  its  original  position, 
while  no  increase  of  lateral  pressure  was  shown  by  the 
side  diaphragm,  there  was  a  very  large  increase  of  pres- 
sure on  the  bottom  diaphragm,  or  sufficient  to  cause  the 
water  to  flow  out  of  the  top  of  the  4-ft.  gage  glass  tube, 
which  was  not,  therefore,  long  enough  to  record  the  pres- 
sure; in  fact,  the  total  weight  of  the  grain  was  then  rest- 
ing on  the  bottom  diaphragm,  and  in  addition  the  grain 
was  acting  as  a  column  to  support  the  weight  of  the  bin 
itself." 

Now  the  lateral  pressure  in  this  experiment  at  the  bot- 
tom of  a  bin  78  ins,  high  was  .1894  Ib.  per  sq.  in.  This 
is  only  one-twelfth  of  the  vertical  pressure  instead  of  being 
six-tenths. 

In  one  of  the  experiments  referred  to  by  Mr.  Ashcroft, 
among  those  made  at  Watertown  Arsenal,  is  one  on  a 
column  reinforced  with  wide  bands.  By  my  count  these 
bands  comes  within  a  half  inch  of  each  other  instead  of 
ein  inch.  This  column  stood  5,289  Ibs.  per  sq.  in.  It 
is  safe  to  say  that  the  concrete  was  in  a  state  bordering 
on  disintegration  under  this  load.  The  lateral  pressure 
on  the  bands  could  not  have  exceeded  a  force  that  would 
stress  the  steel  to  its  ultimate  strength,  and  this  will 
give  us  a  basis  for  determining  that  pressure.  In  the 
2  ins.  of  a  lo-in.  column  occupied  by  one  band  an  equiva- 
lent fluid  pressure  would  be  2  X  5  X  5,289  =  52,890  Ibs.  If 
the  net  area  of  the  band  were  an  eighth  of  a  square  inch, 
the  unit  tension  on  the  basis  of  a  liquid  pressure  would 
be  423,000  Ibs.  I  do  not  know  what  grade  of  steel  was 
used,  but  if  it  were  good  for  80,000  Ibs.  per  sq.  in.  the 
235 


lateral   pressure   could   not   have  been   as   much   as   one- 
fifth  of  the  longitudinal  pressure. 

^Mr.  Ashcroft's  advocacy  of  the  closer  spacing  of  rings 
and  of  wide  rings  leads  to  the  conclusion  that  the  best 
column  is  a  steel  tube  filled  with  concrete.  There  is 
no  doubt  that  this  would  make  a  strong  column,  but  it 
is  a  composite  column,  with  all  that  the  term  implies  in 
the  way  of  uncertainty  in  the  distribution  of  stress,  and 
not  a  reinforced  concrete  column.  There  are  objections 
to  such  a  column  for  ordinary  use  that  it  is  needless  to 
mention. 

The  objection  to  a  flat  bar  in  reinforced  concrete  is 
that  the  holding  power  of  concrete  is  due  to  its  gripping 
the  steel,  rather  than  mere  adhesion.  The  concrete  tends 
to  shrink  away  from  the  side  of  a  broad  flat  bar,  whereas 
it  grips  firmly  a  small  square  or  round  bar.  Further, 
the  concrete  on  the  outside  of  a  broad  flat  bar  near  the 
surface  may  be  easily  knocked  off.  Some  years  ago  I 
observed  some  reinforced  concrete  beams  in  which  the 
reinforcement  was  a  number  of  flats,  which  were  brought 
up  and  hooked  over  the  flanges  of  steel  beams.  The  con- 
crete below  the  bars  fell  off  in  large  chunks  when  the 
forms  were  removed. 

The  objection  to  longitudinal  steel  in  a  column,  that 
is,  to  the  counting  upon  it  as  taking  part  of  the  column 
load,  is  that  this,  too,  makes  the  column  a  composite 
structure  and  not  a  reinforced  concrete  column. 

I  cannot  see  any  objection  to  lack  of  rigidity,  as  it  is 
called,  in  a  column,  that  is,  to  a  column  that  will  shorten 
a  proportionately  large  amount  under  load.  Wooden 
columns  with  a  safe  load  of  1,000  Ibs.  per  sq.  in.  and  E 
=  1,000,000  will  shorten  three  times  as  much  as  steel 
columns  at  10,000  Ibs.  per  sq.  in.  E  =  30,000,000,  but 
wooden  columns  are  not  objectionable  merely  on  this 
account.  In  a  beam  rigidity  is  very  essential,  as  the 
deflection  can  be  felt  or  readily  measured;  but  a  little 
additional  deflection  in  a  column  cannot  be  detected  with- 
out the  most  careful  measurement.  An  explanation  of 

236 


the  lack  of  rigidity  in  reinforced  columns  as  observed 
in  the  Watertown  Arsenal  tests  is  found  in  the  tendency 
of  concrete  to  shrink  in  setting.  It  does  not  seem  to  me 
to  be  necessary  to  assume  that  fissures  occur,  on  this 
theory,  as  suggested  by  Mr.  Howard  (in  Eng.  News,  July 
5,  1906).  The  tendency  to  shrink  may  be  there  and  may 
be  offset  partially  by  the  steel  embedded.  The  concrete 
is  then  like  a  spring  which  is  held  from  contracting  quite 
down  to  its  normal  length  by  the  steel.  Again  the  tend- 
ency to  shrink  away  from  coils  or  hoops  would  make  a 
swelling  out  of  the  column  (due  to  tne  load)  necessary 
before  the  coil  is  brought  into  action. 

Mr.  Ashcroft  says,  "In  a  reinforced  beam  we  place  the 
metal  where  it  will  resist  the  tensile  stresses,  leaving  the 
plain  unreinforced  concrete  to  take  care  of  the  compres- 
sive  stresses  of  500  Ibs.  per  sq.  in.  or  greater."  This  is 
exactly  what  we  ought  to  do  with  columns.  A  short 
block  one  or  two  diameters  in  height  could  safely  be 
loaded  to  500  Ibs.  per  sq.  in.,  but  a  plain  concrete  column, 
if  loaded  to  this  amount,  is  apt  to  break  suddenly  by 
bulging  or  flexure.  The  coils  and  longitudinal  rods  are 
used  to  overcome  this  weakness,  just  as  the  reinforcing 
rods  in  a  beam  are  used  to  overcome  the  weakness  of  the 
beam  in  tension.  The  strength  of  the  concrete  in  either 
case  is  practically  that  of  concrete  in  short  blocks. 

Confined  in  a  cylinder,  concrete  (or  even  loose  sand) 
has  a  very  great  power  for  carrying  loads ;  but  while  this 
fact  is  very  useful  in  some  lines  it  has  little  bearing  on 
reinforced  concrete  design.  . 

Has  Mr.  Ashcroft's  experience  with  sand  jacks  shown 
him  that  the  sand  issues  from  the  gate  with  a  pressure 
approaching  six-tenths  of  the  unit  load  upon  it?  Would 
he  design  the  walls  of  the  jack  for  this  pressure?  Yours 
very  truly, 

Edward  Godfrey. 

Monongahela  Bank  Bldg.,  Pittsburg,  Pa.,  Aug.  31,  1906. 

[In  connection  with  the  explanation,  above  offered,  of 
the  compressibility  of  concrete  columns  in  certain  cases, 

237 


the  old  fallacy  that  two  springs  combined  in  opposition 
are  more  sensitive  than  a  single  spring  recurs  to  mind. 
Really,  the  stiffness  of  two  springs,  whether  in  opposition 
or  in  parallel,  is  the  sum  of  their  individual  rigidities,  as 
a  diagram  will  readily  show.  Now,  applying  this  to  the 
reinforced  concrete,  we  have  the  concrete  in  tension  due 
to  shrinking,  and  the  steel  in  compression  to  an  equal 
amount.  The  rigidity  of  the  combination,  that  is,  the 
load  required  for  unit  compression,  is  just  as  great  under 
these  circumstances  as  if  both  steel  and  concrete  were 
initially  unstressed.  The  only  case  in  which  there  is  an 
exception  to  this  rule  is  when  there  is  a  certain  range  of 
inelastic  motion,  or  when  the  elastic  system  is  changed 
at  a  given  period;  the  former  is  instanced  by  local  crush- 
ing at  the  bearing  surfaces,  the  latter  by  loose  fit  of  one 
of  the  elements  which  operates  to  keep  it  free  from  load 
until  a  certain  compression  is  reached. — Ed.] 


A  FURTHER  NOTE  ON  THE  ANALYSIS  OF  RE- 
INFORCED CONCRETE  COLUMNS 

Sir:  Referring  to  your  comment  on  my  suggested  ex- 
planation of  the  lack  of  rigidity  in  a  reinforced  concrete 
column,  in  Engineering  News  of  Sept.  6,  I  beg  to  suggest 
further  that  the  concrete  is  not  in  all  respects  like  a 
spring,  but  is  restrained  in  the  neighborhood  of  the  steel 
more  than  at  other  points.  Suppose,  for  example,  that 
a  column  of  concrete  with  a  central  longitudinal  rod  be 
molded.  In  setting,  the  concrete  will  tend  to  shrink,  and 
near  the  outer  edge  of  the  column  this  shrinkage  will 
actually  occur,  in  practically  full  amount.  But  near  the 
steel  the  shrinkage  will  be  counteracted  by  the  resistance 
of  the  steel  to  compression,  and  only  a  small  part  of  the 
normal  shrinkage  will  take  place,  resulting  in  longitudinal 
tension  in  this  zone  of  concrete,  and  longitudinal 
compression  in  the  steel.  The  end  faces  of  the  column 
will,  therefore,  not  be  planes,  but  will  be  low  at  the  per- 

238 


iphery,  while  the  end  face  of  the  steel  rod  will  be  the 
highest  point.  Hence,  when  the  column  is  put  in  the 
testing  machine  for  a  compression  test,  the  load  on  the 
end  blocks  will  be  received  by  the  steel  and  the  imme- 
diately surrounding  concrete  before  the  concrete  away 
from  the  steel  receives  its  load.  The  concrete  near  the 
steel  would  therefore  be  under  greater  unit  stress,  and 
the  apparent  rigidity  might  be  less  than  plain  concrete. 
The  case  of  a  spring  was  cited  to  show  that  it  is  not 
necessary  to  assume  that  fissures  exist  where  the  concrete 
is  not  shrunk  down  to  its  normal  size.  Yours  very  truly, 

Edward  Godfrey. 
Pittsburg,  Pa.,  Sept.  7,  1906. 


The  Designing  of  Reinforced  Con- 
crete Retaining  Walls. 

The  lateral  pressure  of  earth  -is  too  uncertain  to  be 
defined  by  any  law,  and  hence  a  correct  theory  for  pro- 
portioning a  retaining  wall  in  the  general  sense  of  the 
term  is  not  possible.  Some  earths  will  remain  vertical 
for  some  time  without  any  confining  structure;  some 
will  even  stand  tunneling  without  caving  in.  A  board 
fence  will  retain  a  considerable  height  of  earth  laid 
against  it  for  awhile.  On  the  other  hand,  slips  are  liable 
to  occur  in  earth  after  it  has  stood  for  some  time  un- 
supported. These  often  exert  great  force. 

The  lateral  force  of  grain  is,  no  doubt,  nearly  con- 
stant for  a  given  kind  of  grain  under  given  conditions. 
The  same  is  probably  true  of  sand,  if  one  of  the  condi- 
tions be  a  definite  proportion,  or  the  entire  absence,  of 
moisture.  But  in  the  case  of  the  substances  generally 
classed  under  the  term  earth  there  is,  as  intimated,  a 
variety  of  states,  ranging  from  soft  mud  that  will  exert 
a  lateral  pressure  approximating  a  fluid  pressure,  to  shales 
that  exert  no  active  lateral  pressure.  A  condition  ap- 
proximating a  fluid  pressure  ought  to  be  avoided  in  any 


good  design  by  proper  drainage.  Two  cases  calling  for 
special  exercise  of  judgment  are  (i)  the  one  mentioned, 
of  shale,  which  is  itself  a  sort  of  retaining  wall  of 
little  durability,  and  (2)  a  case  where  large  slips  are 
probable,  either  due  to  an  inclination  of  the  under 
lying  rock  toward  the  retaining  wall,  or  to  a  heavy  sur- 
charge, that  is,  earth  sloping  steeply  above  the  top  of 
the  wall. 

This  paper  treats  of  a  wall  to  retain  ordinary  fill  or 
prevent  natural  earth  from  slipping.  The  most  severe 
test  of  a  retaining  wall  is  usually  the  freezing  and  thaw- 
ing of  the  earth  around  it.  The  forces  produced  thereby 
are  quite  indeterminate.  They  can,  however,  be  largely 
diminished  by  drainage.  It  has  been  found  that  masonry 
walls  having  a  base  one-third  the  height  of  the  earth 
retained  will  resist  these  forces  and  retain  any  ordinary 
earth  with  complete  rigidity.  That  this  relation  between 
the  base  and  height  agrees  with  the  theory  of  earth  pres- 
sures commonly  employed  is  shown  by  the  following. 

The  theory  referred  to  is  based  on  deductions  from  the 
assumed  action  of  a  granular  mass  having  no  cohesion 
between  its  particles.  It  is  found  that  the  effect  is 
that  of  a  wedge  of  the  material  sliding  without  friction 
on  a  plane  the  slope  of  which  bisects  the  angle  of  re- 
pose of  the  material  and  the  vertical  back  of  the  retain- 
ing wall.  It  is  customary  in  discussions  on  retaining 
walls  to  treat  the  force  due  to  this  wedge  as  though  it 
were  produced  by  a  solid  block  with  its  center  of  pres- 
sure at  a  distance  of  one-third  of  h  from  the  base.  The 
calculations  are  simplified  by  treating  it  as  a  liquid  pres- 
sure, the  weight  of  the  liquid  per  cubic  foot  being  a 
certain  fraction  of  the  actual  weight  of  the  earth.  This 
fraction  is  equal  to  the  square  of  the  tangent  of  the 

angle  —  (Fig.   i),  a  being  the  complement  of  the  angle 

of  repose. 

The  angle  of  repose  of  ordinary  earth  is  about  45°, 
half  of  its  complement  is  22^°,  and  the  square  of  the 

240 


tangent  of  22^°  is  .1716,  or  nearly  one-sixth.  Hence  if 
we  ase  the  pressure  of  a  liquid  having  a  density  one- 
sixth  that  of  earth  we  will  have  the  effect  of  this  lateral 
pressure  so  far  as  horizontal  forces  are  concerned.  This 
will  neglect  the  vertical  component  of  the  force  of  this 
sliding  block.  A  small  and  uncertain  amount  of  this 
vertical  component  would  act  in  friction  on  the  back 
of  the  wall;  the  remainder  would  be  carried  on  the  in- 
clined surface  upon  which  the  block  slides.  As  the 
force  of  friction  tends  to  give  greater  stability  to  the 
wall,  it  is  on  the  side  of  safety  to  neglect  it. 


Fig.  1.    Diagram  of  Earth  Pressure  Against  a  Retaining 
Wall  with  Vertical  Face. 

Now  from  Fig.  i,  if  we  take  moments  around  X  and 
use  as  the  weight  of  earth  100  Ibs.  per  cu.  ft.,  and  of 
masonry  150  Ibs.  per  cu.  ft.,  we  have  for  stability  the 
following  equation  of  moments: 


from  which  we  find 

h  =  3    b. 

Hence,  using  only  the  horizontal  forces  and  neglecting 
adhesion  or  friction  on  the  back  of  the  wall,  we  find 
that  a  wall  having  a  height  three  times  its  base,  which 
is  usually  considered  in  good  proportion  for  a  retaining 
wall,  will  be  found  to  be  stable  against  ordinary  earth. 

In  retaining  walls  of  reinforced  concrete  the  earth 
itself  may  be  utilized  to  prevent  the  overturning  of  the 

241 


wall,    not    by    its    uncertain    friction    or    adhesion    but    by 
its  weight. 

A  form  of  reinforced  concrete  retaining  wall  coming 
into  use  is  composed  of  a  front  curtain  wall  and  a  bot- 
tom slab,  both  reinforced  with  horizontal  rods;  wall  and 
slab  are  united  by  ribs  at  intervals.  Fig.  2  is  a  modifi- 
cation of  that  style  of  construction,  by  the  addition  of 
steps  at  the  junction  of  the  front  wall  and  the  bottom 
slab.  The  purpose  of  these  steps  will  be  made  evident 
further  on.  The  ribs  are  spaced  a  fixed  distance  apart, 
the  same  for  all  heights  of  wall.  The  design  is  to  be 
used  only  for  walls  having  a  base  width  of  5  ft.  or 


Pozfs"E' '  E>-fenct  from  Top 
fff  WaU  to  Toe:  r 


Fig.  2-  Design  for  a  Standard  Re- 
taining Wall  of  Reinforced  Concrete, 
for  any  Base  not  less  than  5  ft. 

(Dimensions  of  parts  are  given  in 
terms  of  width  of  base.  Steel  stress, 
12,500  Ibs.  per  sq.  in.  Beam  reinforce- 
ment not  to  exceed  l/£  per  cent.) 


242 


more.  The  reason  for  the  5-ft.  lower  limit  of  base  and 
for  the  constant  spacing  of  ribs  will  be  shown  in  a  later 
paragraph. 

In  designs  that  have  been  illustrated  in  engineering 
publications,  two  sets  of  rods  are  shown  in  the  bottom 
slab,  one  near  the  bottom  of  slab  and  the  other  near 
the  top,  both  spaced  uniformly  for  the  full  width.  The 
writer  believes  this  to  be  unnecessary  and  uneconomical. 
The  execution  of  the  work  is  greatly  complicated  thereby, 
and  the  forces  are  not  present  demanding  this  re- 
inforcement. While  it  is  true  that  this  slab  is  contin- 
uous, and  while  somewhat  less  moment  is  found  by  con- 
sidering it  as  continuous,  the  purposes  of  good  construc- 
tion are  better  served  by  proportioning  the  slab  for  the 
full  moment  as  a  simple  beam  and  then  adding  some 
short  rods  in  the  top  flange  running  across  the  support 
to  relieve  the  concrete  of  tension. 

The  standard  wall  shown  in  Fig.  2  was  evolved  as  a 
result  of  investigation  to  determine  the  proportions  of 
a  reinforced-concrete  wall  that  would  be  stable  against 
earth  pressure  on  the  same  basis  as  a  solid  masonry  wall, 
granting  that  the  latter  will  be  stable  if  made  with  a  base 
one-third  of  its  height.  Three  walls  were  taken,  having 
bases  5,  10  and  15  ft.  respectively,  and  heights  12,  24 
and  36  ft.  respectively,  with  other  dimensions  as  given 
in  Fig.  2.  The  volumes  per  bay  were  found  to  be  96.6, 
452.8  and  1,168.5  cu.  ft.  respectively.  Solid  masonry 
walls  of  the  same  heights  and  having  bases  one- 
third  the  height  would  contain  3.73,  3.39  and  3.14 
times  as  much  in  volume  of  masonry  respectively  as  the 
concrete-steel  walls;  hence  if  reinforced  concrete  does 
not  cost  more  than  three  of  four  times  as  much  as  solid 
masonry  or  plain  concrete,  the  former  is  the  more 
economical  in  the  form  of  retaining  walls.  The  addi- 
tional excavation  for  the  wider  base  may  enter  as  a  fac- 
tor in  the  relative  costs.  It  is  not  the  purpose  to  give 
actual  relative  costs,  but  only  to  show  that  there  is  a 
243 


large  margin  in  favor  of  the  reinforced-concrete  retain- 
ing wall.  * 

The  centers  of  gravity  of  these  three  walls  were  found 
to  be  1.43  ft.,  3.00  ft.  and  4.66  ft.  respectively  from  the 
heel  of  wall.  The  respective  volumes  of  earth  over  the 
slab  are  332.3,  1,377.2  and  3,206.3  cu.  ft.  The  centers 
of  gravity  of  these  volumes  are  located  2.96  ft,  5.97  ft. 
and  9.01  ft.  respectively  from  the  heel  of  wall.  The 
moments  of  stability  of  these  three  walls,  taken  about  a 
point  one-third  of  the  base  from  the  heel,  were  found 
to  be  39,599,  340,405  and  1,227,272  ft.-lbs.  respectively,  at 
100  Ibs.  and  150  Ibs.  per  cubic  foot  for  earth  and  concrete 
respectively.  The  earth  load  considered  is  that  directly 
over  the  bottom  slab  up  to  the  level  of  the  top  of  wall. 
Assuming  that  the  force  of  the  earth  back  of  the  wall 
is  that  of  a  liquid  one-sixth  of  its  density  the  weight  of 
a  cubic  foot  of  earth  to  balance  the  above  moments  would 
be  no,  in  and  in  Ibs.  respectively. 

One  peculiarity  respecting  these  three  walls  is  that  the 
resultant  center  of  gravity  of  earth  and  concrete  is  in 
each  case  almost  exactly  in  the  center  of  the  slab.  This 
makes  it  proper  to  assume  that  the  pressure  due  to  the 
weight  is  uniformly  distributed  over  the  base,  as  shown 
at  a,  Fig.  2,  as  the  stiffness  of  the  bottom  slab  is  suffi- 
cient to  give  this  distribution.  The  reaction  of  the  earth 
under  the  slab  will  be  uniformly  varying  from  zero  in- 
tensity at  the  toe  of  wall  to  double  the  intensity 
of  the  uniform  load  at  the  heel  of  the  wall?  as  at  b 
The  difference  between  these  sets  of  forces,  or  the  forces 
as  shown  at  c,  must  be  resisted  by  internal  stresses  in 
the  concrete.  On  the  left  half  of  the  bottom  slab  the 
forces  are  seen  to  be  upward.  If  the  construction  were 
a  reinforced  slab,  it  would  require  the  principal  rein- 
forcement in  the  upper  part.  For  simplicity  of  construc- 
tion it  is  desirable  to  avoid  this.  The  close  proximity 
of  the  vertical  wall  makes  it  possible  to  throw  this  force 
directly  into  that  wall  by  means  of  the  steps  at  the  junc- 
tion of  wall  and  slab.  These  steps  could  of  course  be 
244 


replaced  by  a  chamfer  or  slope,  if  the  latter  were  found 
to  be  simpler  of  construction. 

On  the  right  half  of  the  bottom  slab  there  is  a  vertical 
load  downward  varying  in  intensity  from  zero  at  middle 
to  an  amount  at  the  edge  of  slab  which  may  be  taken  as 
the  weight  of  superimposed  earth  and  of  the  slab  itself. 
This  is  close  to  250  X  b  ^s-  Per  SQ-  ft-  Taking  the  effec- 
tive span  of  the  slab  as  7^  ft.  the  bending  moment  on  the 
extreme  right  edge  is  250  b  X  7T/^  X  7^  -^  8  =  x>758  b- 
This  is  in  foot-pounds  per  foot  width  of  slab. 

In  order  to  give  clearance  for  the  angles  shown  in  Fig.  2, 
the  steel  rods  are  placed  one-sixth  of  the  depth  of  slab 
from  the  bottom.  Following  the  method  employed  by  the 
writer,  and  described  in  Engineering  News,  March  15, 
1906,  the  effective  depth  of  the  slab  is  found  to  be  2/3  of 
its  depth.  But  as  the  depth  of  slab  is  3/20  b,  its  effective 
depth  (that  is,  the  distance  from  center  of  steel  to  center 
of  compression  in  concrete)  is  i/io  b.  For  an  area  of 
steel  =  A,  in  sq.  in.  per  foot  width  of  slab,  and  a  stress 
of  12,500  Ibs.  per  sq.  in.  we  have  an  allowed  bending 
moment  of  12,500  A  X  I/I°  ^  —  1*250  A  b  foot-pounds. 

Equating  this  to  1,758  b,  found  above,  we  have 
A  =  1.406. 

This  can  be  made  up  of  four  ^-in.  diameter  rods.  It  is 
thus  seen  that  for  any  size  of  retaining  wall  5^-in.  round 
rods  spaced  3  ins.  apart  will  take  the  tensile  stress  in  the 
bottom  slab  at  the  extreme  right  edge. 

When  the  area  of  steel  does  not  exceed  i%  per  cent  of 
that  of  the  concrete  in  the  slab  (see  article  above  referred 
to)  the  stress  on  concrete  will  be  within  safe  limits.  It  is 
seen  that  the  area  A  found  above  is  \Y$  per  cent  of  that 
of  a  slab  12  ins.  wide  and  9.4  ins.  deep.  For  a  base  of  5  ft. 
the  depth  of  slab  is  9  ins.;  hence  a  lower  limit  of  about 
5  ft.  should  be  adhered  to  for  this  standard.  For  smaller 
walls  the  thickness  of  parts  for  a  wall  of  5-ft.  base  could 
be  maintained  and  the  span  between  ribs  varied  to  suit 
the  bending  moment  found.  Thus,  for  a  wall  having 
2^-ft.  base  (one-half  of  the  standard  5-ft.  wall),  the  load 

245 


on  the  slab  will  be  approximately  one-half  of  that  on  the 
S-ft.  wall.  (The  height  of  this  wall  would  be  6  ft.)  A 
9-in.  slab  with  the  standard  reinforcement  will  be  good 
for  a  span  ^  "2"  times  the  standard,  or  10.6  ft,  say  10  ft. 
clear. 

The  span  of  7  ft.  in  the  standard  wall  is  found  as  fol- 
lows: Let  s  =  clear  span  in  feet.  The  end  shear  on  one 
foot  of  width  of  the  slab  is  250  b  X  Vz  s  :=  125  b  s.  The 
shearing  strength  of  a  slab  3-20  b  feet  deep  and  one  foot 
wide,  at  40  Ibs.  per  sq.  in.  on  the  gross  area  is 
3-20  b  X  12  X  I2  X  40  =  864  b. 

Then  from  the  equation 

125  b  s  =  864  b, 
we  find  s  =  6.91  ft. 

Since  this  remains  true  for  all  sizes  of  standard  walls, 
it  is  seen  that  the  shear  is  taken  care  of  also  in  walls  of 
less  than  5  ft.  in  base,  as  the  slabs  will  have  a  greater 
relative  depth  than  in  the  standard  walls. 

The  reinforcement  in  front  wall  is  found  as  follows:  It 
will  be  seen  in  the  standard  retaining  wall  that  the  depth 
from  top  of  wall  to  top  of  steps  is  i.gb.  The  intensity  of 
horizontal  pressure  is  therefore  1.9  b  X  *~6  X  IO°  ^s- 
per  sq.  ft.  This  gives  a  moment  on  a  foot  depth  of  wall 
—  223  b  ft. -Ibs.  The  moment  of  resistance  of  the  con- 
crete-steel slab,  found  as  above,  is 

12,500  A  X  —X  —=SM  A  b. 

From 

223  b  =  833  A  b, 
we   have  A  =  .267  sq.  in. 

This  would  be  made  up  by  one  §^-in.  round  rod  for 
every  foot  of  depth  of  wall.  This  reinforcement  is  carried 
up  to  the  top  of  the  wall  and  is  used  as  indicated  on  the 
lower  portion  of  the  wall  and  on  the  bottom,  though  theo- 
retically less  reinforcement  would  be  required.  The  pur- 
pose is  to  tie  the  wall  together. 

The  rods  in  the  rib  act  to  tie  together  the  bottom  slab 

246 


and  the  vertical  wall,  the  manifest  tendency  being  for 
these  to  pull  against  each  other.  The  chief  use  of  the 
concrete  in  the  ribs  is  to  protect  these  rods.  It  is  essen- 
tial that  the  rods  have  an  efficient  end  anchorage,  and 
any  other  anchorage  or  bond  can  serve  only  a  subsidiary 
purpose.  The  line  of  cleavage  in  the  rib  may  be  im- 
mediately above  the  bottom  slab,  and  practically  the  whole 
strength  of  the  rod  is  needed  at  that  plane.  In  the  short 
depth  of  the  slab  there  is  not  length  enough  for  even  me- 
chanical bond  to  take  effective  hold  for  the  full  strength 
of  the  rods.  Hooks  or  curves  on  the  ends  of  rods  have 
not  been  shown  by  tests  to  be  effective  end  anchorages. 
Such  a  detail  would  not  be  accepted  in  structural  steel  work. 
The  use  of  plain  round  rods  with  thread  and  nut  at  end, 
attached  to  a  front-to-back  angle  in  the  bottom  of  the 
slab,  as  shown  in  Fig.  2,  seems  to  be  the  most  economical 
as  well  as  the  most  effective  means  of  meeting  these  con- 
ditions. These  angles  may  also  act  as  anchors  for  the 
horizontal  rods,  at  ends  of  wall,  if  any  such  anchorage 
is  needed. 

The  angles  serve  to  locate  the  rods  properly  and  to  hold 
them  in  position  against  displacement  during  the  placing 
of  the  concrete.  They  also  make  it  more  difficult  to  omit 
any  rods  and  easy  to  detect  any  omissions.  All  of  these 
points  are  of  great  weight  in  construction  where  unskilled 
labor  is  so  commonly  employed. 

The  rods  in  the  rib  take  the  downward  force  shown  at  c, 
Fig.  2,  the  amount  of  which  at  the  right  edge  is  at  a 
rate  per  foot  close  to  250  b  X  7  =  !>75o  b  Ibs.  On  a  re- 
taining wall  of  5 -ft.  base  the  load  in  a  foot  is  8,750  Ibs. 
At  12,500  Ibs.  per  sq.  in.  this  would  require  four  rods 
^-in.  in  diameter.  For  a  10-ft.  base  four  n-i6-in.  round 
rods  are  required,  etc.  By  giving  these  rods  the  same 
horizontal  spacing  at  bottom  as  those  in  the  bottom  slab 
and  varying  the  rate  of  spacing  in  the  same  manner,  the 
vertical  load  is  taken  care  of. 

These    rods    start    vertical;    hence    the    vertical    load- 

247 


measures  their  stress  and  not  the  component  in  a  diagonal 
direction.  Their  stress  is  not  uniform  throughout,  but 
they  begin  near  the  foot  of  the  wall  to  transmit  their  stress 
into  the  concrete  to  resist  the  upward  thrust  of  the  forces 
on  the  left  half  of  the  base.  Their  radius  of  curvature 
should  not  be  less  than  about  twenty  times  their  diameter, 
so  that  the  unit  pressure  exerted  by  the  side  of  rod  on 
the  concrete  will  not  exceed  safe  limits.  (A  square  rod 
curved  to  a  radius  twenty  times  its  diameter  will  exert  a 
radial  force  on  its  side  one-twentieth  of  the  intensity  of 
its  tension,  which  is  the  usual  ratio  between  the  allowable 
stresses  in  steel  and  concrete.  The  use  of  sharp  bends 
in  embedded  rods  is  a  structural  fault  often  met  with.) 

The  rods  should  have  two  nuts  on  the  ends,  so  that  the 
end  nut  can  be  drawn  to  a  tight  bearing  on  the  angle. 
Horizontal  rods  should  be  spliced  by  sleeve  nuts. 

A  modification  of  the  design  can  be  made  in  which  the 
rods  in  rib  pass  through  slotted  (or  large  sized  punched) 
holes,  and  have  cast  iron  beveled  washers.  The  rods  can 
then  be  straight.  The  inclination  would  be  such  as  to 
give  about  8  per  cent  more  stress  than  found  in  vertical 
rods. 

The  gripping  of  concrete  is  sufficient  to  make  up  for 
the  difference  in  strength  of  rod  at  root  of  thread  and 
that  of  the  full  section. 

Anchors  that  take  the  full  stress  of  rods  should  have 
their  areas  twenty  times  the  section  of  the  rod.  This  con- 
dition would  govern  the  size  of  the  flange  of  angle  to  which 
rods  in  the  rib  connect.  These  angles  could  vary  from 
about  2^  X  2^  X  5-i6-in.  for  small  sized  walls  to  4  X 
3  X  £6-m-  f°r  large  walls. 

The  formulas  ordinarily  given  for  continuous  beams  are 
for  beams  having  a  uniform  moment  of  inertia.  If  the 
beams  have  not  a  uniform  moment  of  inertia,  the  formula 
does  not  hold.  If  a  beam  be  purposely  designed  so  as 
not  to  have  a  uniform  moment  of  inertia,  it  will  deflect 
more  at  the  section  not  reinforced  for  the  full  moment, 
248 


and  thus  put  greater  moment  on  the  fully  reinforced 
section.  This  is  the  basis  for  the  somewhat  arbitrary  re- 
inforcement of  the  upper  part  of  bottom  slabs.  The  bend- 
ing moment  at  the  middle  of  this  slab  cannot  exceed  that 
for  a  simple  span.  The  upper  rods  are  added  to  prevent 
cracking,  and  consequent  weakening  of  the  slab  in  shear, 
near  the  ribs. 

It  is  recommended  that  long  walls  be  concreted  from 
one  end  to  the  other,  and  not  uniformly  from  the  ground 
up;  so  that  the  shrinking  of  the  concrete  as  it  sets  will 
not  act  on  the  whole  length  of  the  wall  at  once.  It  is 
also  recommended  that  at  expansion  joints,  say  about 
every  100  to  150  ft.,  a  complete  separation  be  made  in  the 
wall,  with  an  end  rib  in  each  portion  of  the  wall. 


THE  DESIGN  OF  REINFORCED-CONCRETE 
RETAINING  WALLS 

Sir:  The  article  in  your  issue  of  Oct.  18,  by  Edward 
Godfrey,  on  the  "Design  of  Reinforced  Concrete  Retain- 
ing Walls,"  was  of  especial  interest  to  the  writer^  because 
it  so  closely  conformed  to  the  methods  of  design  lately 
developed  by  him  in  checking  the  computations  for  a 
very  high  and  long  wall  about  which  he  was  consulted. 

Differences  of  opinion  may  exist  as  to  proper  methods 
of  determining  the  lateral  pressures  exerted  by  earths  of 
different  qualities,  and  as  to  the  proper  design  of  rein- 
forced concrete  beams,  etc.,  but  certain  fundamental 
principles  exist  in  accordance  with  which  every  proper 
design  should  be  prepared,  and  it  seems  to  the  writer 
that  Mr.  Godfrey  has  come  nearest  to  stating  them  of 
any  one  with  whom  the  writer  is  acquainted. 

The  writer's  experiments  on  lateral  earth  pressures,  re- 
ported to  the  American  Society  of  Civil  Engineers,  led  him 
to  the  opinion  that  the  angle  of  surface  repose  for  most 
earths  is  entirely  different  from  the  angle  of  internal 
friction  of  the  same  earths.  Manifestly  it  is  the  latter 
249 


t 

k 

k- 
k- 


(A) 


(E) 


K 


(F) 


(G) 


(H) 


1 

ft'* 


(J) 


\ 

I        \ 
1          \ 


UH  1  i  N  I 

H        iiUH 
^:iii  iL^ji:^:^ 


250 


which  should  be  used  in  most  design  work  instead  of  the 
former.  The  writer  agrees  with  Mr.  Godfrey,  however, 
that  the  actual  active  pressures  may  with  sufficient  ac- 
curacy be  considered  as  fluid  in  effect,  and  a  certain  per- 
centage of  the  weight  of  the  earth  backing  in  amount. 
The  experiments  above  referred  to  seemed  further  to 
show  that  for  walls  more  than  about  5  ft.  high  the  pres- 
sures varied  practically  as  the  depth,  so  that  their  re- 
sultant might,  with  sufficient  accuracy,  be  considered 
as  acting  at  the  lower  third  point  of  the  height  of  the 
wall.  For  walls  of  less  height,  however,  this  point  of  ap- 
plication rose  often  to  a  point  four-tenths  of  the  hei^nt 
above  the  base.  In  most  walls,  then,  the  lateral  pressures 
would  be  represented  by  a  triangular  diagram  of  hori- 
zontal arrows,  having  a  horizontal  base  (sketch  A). 

The  writer  is  in  direct  accord  with  Mr.  Godfrey  where 
he  uses  a  bottom  slab  weighted  by  the  superimposed 
earth,  and  agrees  that  the  resultant  downward  pressure 
of  the  earth  on  this  slab  may,  for  all  practical  purposes, 
be  considered  as  uniform  (sketch  B)  unless  the  design 
employs  a  greatly  extended  toe,  as  is  often  necessary 
with  high  walls  on  soft  soils. 

He  also  agrees  with  Mr.  Godfrey  that  many  designs 
are  faulty  in  the  arrangement  of  the  reinforcement  in  the 
bottom  slab,  probably  from  wrong  assumptions  as  to  the 
distribution  of  the  resisting  earth  pressures. 

While  some  experiments  lately  carried. out  by  the  writer 
(which  are  now  being  repeated)  shed  some  new  light 
on  the  distribution  of  resisting  earth  pressures  under 
walls  and  foundations,  still  for  the  moment  a  uniformly 
varying  distribution  may  be  assumed,  and,  provided  the 
resultant  of  the  two  series  of  forces  above  described  in- 
tersects the  base  of  the  wall  at  the  front  edge  of  its 
middle  third,  the  variation  is  from  zero  at  the  back  to 
twice  the  average  at  the  front  (sketch  C). 

The  diagram  of  resultant  forces  on  the  slab  will  then 
evidently  be  two  triangles,  as  described  by  Mr.  Godfrey 
(sketch  D). 

251 


The  horizontal  forces  are,  of  course,  resisted  by  the 
sliding  friction  between  the  base  of  the  wall  and  the  earth 
beneath,  and  by  the  pressure  of  the  toe  of  the  wall 
against  the  earth  in  front  of  it.  '  This  front  pressure 
may  be  considered  as  distributed  uniformly  over  the  base 
like  the  friction,  for  sake  of  convenience. 

These  assumptions  take  care  of  all  the  external  forces. 

If  the  slabs  in  front  and  base  are  to  be  tied  directly 
together  by  diagonal  rods  in  the  counterforts,  these  rods 
must  be  given  varying  slopes  (approximately  as  at  E  in 
the  sketch  herewith)  to  correspond  with  the  varying  pres- 
sures in  front,  while  their  bottom  ends  must  be  simi- 
larly spaced  to  correspond  with  the  resultant  downward 
earth  pressure.  Then,  too,  these  rods  would  have  quite 
different  stresses  due  to  their  varying  slopes,  so  that  the 
proper  distribution  of  diagonal  rods  of  uniform  diameter 
is  a  very  complicated  affair  to  determine.  Evidently,  if 
some  satisfactory  arrangement  of  horizontal  and  vertical 
rods  can  be  devised  to  produce  the  same  effect  several 
advantages  will  be  gained.  Even  the  arrangement  pro- 
posed by  Mr.  Godfrey  (the  correctness  of  the  design  of 
which  the  writer  strongly  questions)  is  rather  costly  in 
execution,  because  simple  horizontal  and  straight,  approxi- 
mately vertical  rods  are  much  more  easily  placed  by  in- 
experienced labor. 

Such  horizontal^  and  vertical  rods  in  the  counterforts, 
if  spaced  to  correspond  with  the  assumed  forces,  will 
have  a  uniformly  varying  spacing  one  way  to  correspond 
with  that  which  theoretically  should  exist  on  the  face, 
and  a  similar  one  in  an  approximately  vertical  position 
the  other  way,  the  upper  ends  of  the  rods  running  to  all 
points  along  the  back  of  the  counterfort,  while  their 
lower  ends  cover  that  part  of  the  base  over  which  the 
resultant  earth  pressure  is  assumed  as  acting  downward 
(see  sketch  F).  These  rods  simply  carry  to  points  within 
and  along  the  backs  of  the  counterforts  the  active  earth 
stresses,  so  that  the  resultant  diagram  may  be  drawn 
252 


as  shown  at  G  when  primary  stresses  alone  are  con- 
sidered, and  as  at  H  when  the  resultant  earth  pressures 
and  rod  actions  are  considered. 

Now  the  concrete  in  the  counterforts  being  highly  re- 
sistant to  compressive  stresses,  easily  resists  the  com- 
bined action  of  these  loads  and  the  whole  counterfort  is 
much  better  tied  together  than  in  Mr.  Godfrey's  design. 
The  latter  seems  a  little  inconsistent  in  not  better  rein- 
forcing the  counterforts  after  employing  more  steel  than 
theory  requires  at  several  other  points.  A  similar  incon- 
sistency crops  out  in  the  omission  of  any  steel  in  the 
steps  which  are  supposed  to  carry  over  into  the  face  of 
the  wall  the  upward  pressure  near  the  front  under  the 
bottom  slab.  Unless  the  concrete  is  considered  as  taking 
some  tensile  stress,  reinforcement  should  be  employed 
in  some  manner  in  these  steps,  either  to  make  them  act 
as  beams  of  variable  depth  carrying  the  upward  pressure 
to  the  counterforts,  or  as  brackets  attached  to  the  inside 
of  the  front  face.  Under  the  latter  assumption  horizontal 
rods  perpendicular  to  the  face  should  be  introduced  in  the 
bottom  slab.  These  rods  should  also  be  carried  through 
the  plane  of  the  face  and  into  the  toe  projection,  which 
must  often  be  greatly  extended,  and  the  design  of  which 
Mr.  Godfrey  does  not  consider  even  though  he  shows  such 
a  toe  in  his  diagrams. 

If  the  remainder  of  the  bottom  slab  outside  the  stepped 
portion,  besides  acting  as  a  vertical  beam  to  take  earth 
pressures,  is  considered  as  a  horizontal  beam  designed  to 
resist  the  stresses  which  the  lateral  rods  might  be  intro- 
duced to  resist;  then  proper  additional  ties  should  be 
introduced  in  the  counterforts.  Mr.  Godfrey's  angle  iron 
would  not  seem  of  sufficient  size  to  cover  the  usual  needs. 

It  is  believed,  further,  that  the  practical  construction 
of  the  forms  for  Mr.  Godfrey's  stepped  wall  will  be  more 
costly  than  for  a  wall  without  the  steps  and  with  steel 
introduced  instead. 

Whenever  the  weight  of  a  cubic  foot  of  the  earth  back- 
ing multiplied  by  the  height  of  wall  exceeds  half  the  safe 
253 


bearing  power  of  the  soil,  an  extended  toe  must  be  em- 
ployed. In  that  case  the  diagram  of  vertical  stresses 
may  be  assumed  as  in  sketch  /  and  the  resultant  down- 
ward effect  on  the  bottom  slab  may  or  may  not  reach  zero 
behind  the  face.  A  diagram  somewhat  like  that  of  sketch 
K  will  result. 

In  this  case  the  rods  in  the  counterforts  which  are  de- 
signed to  carry  these  vertical  resultant  stresses  will  them- 
selves be  nearly  or  quite  vertical.  The  exactly  vertica/ 
condition  would  occur  when  the  resultant  earth  pressure 
becomes  zero  under  the  face  of  the  wall,  which  condi- 
tion would  take  place  when  the  toe  is  extended  a  distance 
outside  this  point  approximately  three-tenths  of  the  total 
width  of  base.  This  amount  may  seem  rather  large,  but 
is  not  unknown. 

With  such  an  extended  toe  a  series  of  steps  in  the  out- 
side of  the  wall  would  be  very  proper  because  no  coun- 
terforts are  available,  and  since  the  face  of  the  wall  is 
in  close  proximity.  Properly  arranged  steel  would  be 
very  necessary  unless  tension  is  to  be  allowed  on  con- 
crete. 

What  Mr.  Godfrey  says  wth  regard  to  end  anchorage 
of  rods,  the  writer  believes  to  be  eminently  correct,  ex- 
cept that  the  writer's  experiments  have  shown  that  proper 
hooks  are  entirely  satisfactory.  The  writer  further  agrees 
with  Mr.  Godfrey  in  always  advocating  steel  in  beams 
and  slabs  to  take  up  reverse  moments  at  points  of  support, 
except  that  he  feels  that  the  design  of  the  slabs  as  simple 
beams  with  extra  reverse  reinforcement  added,  is  erring 
too  much  on  the  side  of  safety  even  with  regard  to  the 
exceedingly  uncertain  knowledge  we  now  possess  as  to 
earth  pressures  and  reinforced  concrete  continuous  beams. 

The  writer  has  been  greatly  interested  in  Mr.  Godfrey's 
design,  but  considers  that  the  one  briefly  described  above 
is  more  logical  and  more  economical  of  execution,  espe- 
cially as  to  labor.  Yours  truly,  E.  P.  Goodrich. 

1170  Broadway,  New  York,  N.  Y.,  Oct.  18,  1906. 
254 


THE   DESIGN   OF   REINFORCED   CONCRETE   RE- 
TAINING WALLS 

Sir :  Kindly  permit  me  space  to  reply  briefly  to  Mr. 
E.  P.  Goodrich  in  his  criticism  (Eng.  News,  Nov.  15) 
of  my  article  on  design  of  reinforced  concrete  retaining 
walls  (Eng.  News,  Oct.  18,  1906). 

As  to  the  placing  of  straight  horizontal  and  vertical 
rods  being  simpler  than  the  inclined  rods  used  by 
me,  my  idea  would  be  to  have  the  rods  and  angles  sent 
cut  and  punched  and  threaded  to  the  site.  The  harp- 
like  arrangement  in  each  rib  or  counterfort  can  be  set  up 
on  the  ground  and  raised  to  position.  A  few  braces  would 
hold  all  in  place,  whereas,  with  all  rods  separate,  each 
would  have  to  be  held  individually,  and  liability  to  dis- 
placement is  multiplied. 

The  total  pressure  against  the  front  slab  is  less  than 
that  against  the  bottom,  hence  with  the  same  rods,  starting 
normal,  there  is  more  than  enough  strength  to  take  all 
of  the  force.  The  occurrence  of  rods  apparently  closer 
than  necessary  near  the  top  of  front  slab  will  give  an 
extra  safeguard  against  such  pressure  as  that  due  to  freez- 
ing of  the  ground,  which  would  be  greatest  near  the  sur- 
face. Extraneous  load  would  probably  effect  a  lateral 
pressure  near  the  surface  only. 

In  the  matter  of  the  projection  in  front  of  the  wall, 
and  of  the  steps  being  without  reinforcement,  it  is  seen 
by  my  sketch  that  the  front  projection  is  only  one-third 
as  broad  as  its  height;  also  the  uplift  under  the  steps 
tapers  down  to  nothing  at  the  foot  of  the  steps.  There 
is  strength  enough  in  the  concrete  to  take  the  resultant 
tension  at  a  very  low  value.  Spread  footings  are  allow- 
able even  in  brick  or  rubble  masonry;  they  ought  to  be 
so  in  monolithic  concrete.  If  there  were  necessity  for  a 
(arge  projection  in  front  of  the  wall,  a  modified  design 
ivould  be  required.  It  was  my  purpose  to  give  a  rational 
analysis  of  the  stresses  and  rational  methods  of  taking 
care  of  them.  Yours  very  truly,  Edward  Godfrey. 

Monongahela  Bank  Bldg.,  Pittsburg,  Pa.,  Nov.  IQ,  1006. 
255 


A  Method  of  Measuring-  Deflections 
in  Floor  Tests. 

[Published  in  Engineering  News,  Aug.  25,   1904.] 

By  the  Author 

The  following  description  of  the  method  employed  to 
measure  the  deflection  of  a  floor  under  test  may  be  of  in- 
terest to  any  who  have  similar  tests  to  make. 

The  floor  tested  was  in  2O-ft.  squares,  and  it  was  desired 
to  obtain  the  deflection  at  the  middle  of  the  square  tested, 
as  well  as  at  the  middle  of  the  side  of  the  square,  or  half 
way  between  the  columns.  To  accomplish  this,  pedestals 
or  uprights  were  made  of  a  single  4  x  4-in.  piece  of  wood 
nailed  to  a  block  about  2  x  12  ins.  by  2  or  3  ft.  long.  These 
were  placed  on  the  floor  at  points  where  the  deflections  were 
to  be  measured,  and  blocks  of  pig  iron  were  placed  upon 
them  to  weight  them  down,  so  as  to  prevent  displacement 
by  the  men  in  loading  the  floor.  Enough  pig  iron  was 
placed  on  each  pedestal  to  make  up  approximately  the  re- 
quired load  for  the  space  which  it  occupied. 

In  addition  to  the  pedestal  there  had  been  placed  2  x  10- 
in.  timbers  which  reached  across  the  floor  space  and  were 
nailed  to  posts  resting  on  the  floor  near  the  columns.  These 
were  about  at  the  level  of  a  man's  head,  so  as  not  to  be  in 
the  way  of  the  men  who  were  loading  the  floor. 

They  were  vertically  over  the  points  at  which  deflections 
were  to  be  taken.  The  uprights  were  placed  so  that  a  flat 
side  of  the  4x4  was  against  the  joist  or  timber  which 
reached  across  the  floor.  On  the  back  of  the  upright  there 
was  tacked  a  sheet  of  stiff  paper,  upon  which  was  ruled  a 
horizontal  line.  On  the  joist  was  tacked  another  sheet  of 
stiff  paper,  the  edge  of  which  had  been  divided  accurately 
into  tenths  of  an  inch.  This  was  set  with  the  zero  of  the 


scale  at  the  horizontal  line  on  the  sheet  tacked  to  the  up- 
right. 

As  the  floor  deflected,  the  amounts  of  the  deflections 
could  be  instantly  read  on  the  scale  to  hundredths  of  an 
inch,  by  estimating  tenths  of  scale  divisions.  The  appara- 
tus is  more  clearly  shown  in  the  accompanying  sketch. 

A  number  of  scales  were  ruled  at  the  same  time  by  tack- 
ing the  sheets  down  on  a  drawing  board  with  about  Vz-'m. 


y                                               2x0"  Joist                < 

Rxper  Scale 
Tacked  to  Joist*. 

^~- 

'I 

i 

< 

I- 
I 
/W 

;^s  | 

PCfperh 

Tacked 
?  Upright*-' 

EN6.  NEWS. 

( 

Pig  j       \lron            } 

( 

^  I'd 

C  J 

( 

j 

^  I3~l  "T 

^  ^ 

\ 

?"x  /?"               I 

Apparatus  for  Measuring  Deflections  of  Floor  Panels 
in  Load  Tests. 

along  the  edge  of  each  exposed.  By  dividing  one  sheet  with 
a  decimal  scale  and  ruling  across  the  exposed  edges  all  were 
made  alike.  The  tenths  could  be  further  divided  into  five 
parts  or  fiftieths  with  a  hard  pencil,  but  no  difficulty  was 
experienced  in  estimating  the  hundredths  with  a  scale  di- 
vided into  tenths. 


257 


Reinforced   Concrete    Engineering  in 
the  Making. 

Concrete-steel  or  reinforced  concrete  construction  is  only 
an  infant  as  yet.  The  relatives  have  not  agreed  upon  a 
name.  Many  want  the  hyphenated  appellation  with  the  old 
family  name  of  steel  retained,  while  others  would  express 
the  office  of  the  steel  rather  than  its  presence. 

To  drop  the  figure,  there  is  much  to  learn  by  the  builders 
of  this  construction,  some  things  that  only  experience  will 
teach,  and  others  that  can  be  wrung  from  known  facts  and 
technical  knowledge  in  kindred  lines.  It  is  the  purpose  of 
this  article  to  point  out  some  of  the  things  that  ought  to  be 
set  up  as  guides  in  the  design  and  execution  of  reinforced 
concrete  constructon,  if  it  is  to  have  a  standing  in  the 
class  of  sound  engineering. 

While  it  is  true  that  the  manufacture  of  reinforced  con- 
crete can  be  accomplished  largely  with  ordinary  labor,  it 
is  also  true  that  this  labor  must  have  strict  supervision  by 
competent  foremen,  who  understand  the  importance  of 
doing  the  work  just  as  the  designer  has  planned  it.  A 
laborer  does  not  understand  the  importance  of  a  small  rod 
in  the  concrete,  and  would  probably  see  no  harm  in  leaving 
some  rods  out;  or  he  might  think  that  the  exact  location 
of  rods  is  a  matter  of  no  importance,  so  long  as  they  are 
present.  The  displacing  of  rods,  either  by  accident  or  de- 
sign (as  to  make  the  placing  of  concrete  more  convenient), 
may  be  the  result  of  an  ignorant  workman's  act  for  which 
he  would  feel  no  guilt  because  of  his  ignorance.  Rods  that 
are  intended  to  lie  close  to  the  bottom  of  a  beam  or  slab 
may  thus  be  placed  at  the  middle  of  its  depth,  resulting  in  a 
great  reduction  in  the  strength,  and  not  improbably  being 
a  cause  of  failure.  Rods  bunched  together,  where  they 
should  be  separated,  is  a  possibility  that  would  result  in  a 
loss  of  gripping  power  in  the  concrete. 

Again  a  laborer  may  wish  to  save  himself  the  handling 
of  cement  and  cut  down  on  the  amount  used;  or,  with  a 
view  of  saving  his  employer  expense,  with  the  latter's  con- 

258 


sent,  a  bag  or  two  of  cement  may  be  left  out  occasionally. 
The  time  of  mixing  or  number  of  turnings  on  the  mixing 
board,  if  hand  mixed,  should  not  be  left  to  any  but  ex- 
perienced and  responsible  persons.  The  uniformity  of 
the  concrete  depends  upon  the  thoroughness  of  mixing  and 
correctness  and  constancy  of  the  amounts  of  the  ingre- 
dients. The  strength  of  the  structure  is  gaged,  in  a  large 
measure,  by  the  uniformity  of  the  concrete. 

An  illustration  of  a  workman's  idea  of  the  possibilities 
of  concrete  is  found  in  the  following:  The  writer  ob- 
served some  work  being  put  in,  where  three  or  four  inches 
of  plain  concrete  was  being  laid  on  an  old  wooden  floor. 
With  the  idea  that  the  floor  had  probably  been  shored  or 
strengthened  for  the  heavy  load  he  asked  the  workman 
what  supported  the  concrete.  The  reply  was,  that  "the 
stuff  didn't  need  any  support,  it  supported  itself." 

Inspection  of  every  part  of  the  work  as  it  progresses, 
by  someone  not  interested  in  the  contractor's  end  of  it,  is 
almost  an  absolute  necessity  The  combination  of  possi- 
bilities of  skimping  and  scamping,  through  ignorance  or 
carelessness,  leaves  the  owner  with  the  small  end  in  the 
probability  line,  unless  he  adopts  suitable  means  to  correct 
this  condition.  A  contractor's  guaranty  that  a  structure 
will  be  built  according  to  specifications,  or  that  it  will  not 
crack  or  deteriorate  in  a  given  period,  is  scant  comfort 
when  a  piece  of  work  shows  defects  upon  its  completion, 
and  the  contractor's  final  estimate  declares  that  the  struc- 
ture is  complete  and  ready  for  use. 

A  guaranty  that  a  structure  will  stand  a  specified  test 
load  is  another  uncertainty  to  which  owners  sometimes  tie. 
A  test  load  on  a  small  square  of  a  large  floor  of  continuous 
construction  is  no  more  a  criterion  of  its  capacity  when 
fully  loaded,  than  the  ability  of  a  tank  to  hold  a  barrel 
is  proof  that  it  will  hold  ten  barrels.  In  the  early  days  of 
bridge  building  it  was  not  unusual  to  see  in  specifications 
a  requirement  that  a  bridge  should  be  loaded  for  a  certain 
period  with  a  given  train  load.  Bridge  builders  have  ad- 
vanced away  beyond  that  point.  It  is  the  man  in  the  de- 

259 


signing  department  that  can  tell  to  a  nicety  what  the  bridge 
is  fit  to  carry,  the  presumption  being  that  all  parts  of  the 
fabrication  of  the  bridge  have  received  the  necessary  in- 
spection, and  the  plans  are  carried  out  in  every  particular. 

Tests  on  reinforced  concrete  construction  are  quite 
proper,  but  they  should  be  made  on  an  isolated  unit  of  the 
floor  not  supported  on  all  sides  by  the  contiguous  con- 
struction; or  else  a  test  to  be  of  value,  should  be  made  on 
a  large  section  of  the  floor  in  place,  of  sufficient  extent  not 
to  be  affected  by  extraneous  support. 

One  contract  which  came  under  the  writer's  notice  called 
for  floors  that  had  a  theoretical  breaking  strength  of  three 
times  a  certain  load  per  square  foot.  The  floors  in  ques- 
tion proved  to  be  unsafe  under  test  with  one  time  this  load 
per  square  foot,  though  by  the  designer's  method  of  figur- 
ing the  "theoretical  breaking  strength"  was  supposed  to 
be  three  times.  The  theoretical  breaking  strength  of 
concrete  or  of  a  concrete-steel  floor  is  too  nebulous  to  have 
any  meaning  in  a  contract. 

An  error  that  works  to  the  detriment  of  reinforced  con- 
crete construction  is  the  notion  that  it  is  the  cheapest  form 
of  construction.  For  many  reasons  it  is  economical,  but 
in  no  sense  is  it  cheap.  Properly  built  it  cannot  compete, 
even  at  present  high  prices,  with  wooden  construction  in 
the  matter  of  first  cost.  It  compares  favorably  in  cost  with 
steel  construction,  and  in  many  situations  structures  can  be 
built  of  reinforced  concrete  for  less  than  of  structural  steel, 
when  the  same  character  of  design  is  maintained. 

The  necessity  for  using  wet  concrete  cannot  be  too 
strongly  urged.  Dry  concrete  is  lacking  in  the  essential 
characteristics  that  make  the  combination  of  steel  and  con- 
crete so  strong  and  durable.  Mealy  concrete  will  be  porous 
and  fail  to  protect  the  steel;  wet  concrete,  if  it  contains 
enough  cement,  will  coat  the  steel  with  a  film  of  cement. 
This  is  one  essential  to  the  preservation  of  the  steel ;  dense 
concrete  is  another.  Neither  of  these  are  possible  with  dry 
concrete.  Dry  concrete  has  not  much  adhesion;  it  will 
therefore  fail  to  take  hold  of  the  steel.  It  is  also  lacking 

260 


in  cohesion,  and  would  therefore  be  weak  in  its  gripping 
power  on  the  steel.  Dry  concrete  will  set  in  a  shorter  time 
than  wet  concrete,  and  on  short  time  tests  will  show  greater 
compressive  strength.  The  wet  concrete  will,  however, 
attain  greater  strength  than  the  dry  concrete  when  it  has 
thoroughly  set.  Many  erroneous  notions  about  the  strength 
of  reinforced  concrete  and  the  preservation  of  the  imbedded 
steel  have  no  doubt  been  the  result  of  the  use  of  dry  con- 
crete, and  the  unsatisfactory  conditions  observed.  Con- 
crete for  this  class  of  construction  should  be  puddled  rather 
than  tamped,  by  means  that  will  work  out  the  air  spaces 
and  make  the  concrete  to  run  into  all  crevices. 

In  the  matter  of  materials  and  the  proportions  of  the 
same  there  is  not  much  difference  of  opinion.  Good,  hard 
and  durable  broken  stone  or  gravel  is  essential  in  stone 
concrete  for  any  purpose.  For  reinforced  concrete  the 
stones  should  be  small,  say  under  an  inch  in  every  dimen- 
sion for  slabs,  beams,  columns,  and  small  arches,  and  larger 
in  size  for  more  massive  work.  The  reason  that  small 
stones  should  be  used  is  that  they  will  pack  better  around 
the  steel  and  not  leave  voids.  Graded  sizes  from  the  largest 
to  the  smallest  are  very  essential  both  in  the  stone  and  in 
the  sand.  Uniformity  in  the  sizes  of  stone  or  grains  of 
sand  is  to  be  guarded  against.  The  larger  parts  leave  voids 
that  only  the  smaller  parts  can  fill,  and  these  leave  voids 
that  still  smaller  parts  are  necessary  to  fill,  and  so  on  down 
to  the  finest  particles  of  cement. 

In  plain  concrete  economy  can  be  effected  by  a  mixture 
that  is  suited  to  the  particular  broken  stone  or  gravel  used. 
In  such  concrete  it  is  only  necessary  to  provide  enough 
sand  to  fill  the  voids  in  the  stone  and  enough  cement  to 
fill  the  voids  in  the  sand.  In  reinforced  concrete  there 
must  be  an  excess  of  cement,  so  that  the  density  of  the 
concrete  will  be  assured,  and  so  that  the  steel  will  be  cov- 
ered with  cement. 

One  part  of  Portland  cement  to  two  parts  of  sand  and 
four  parts  of  broken  stone,  gravel  or  cinders,  all  by  volume, 
is  the  generally  accepted  standard  mixture.  A  leaner 

261 


mixture  than  this  is  not  recommended.  Stone  concrete  of 
these  proportions,  made  of  good  materials,  will  have  a 
compressive  strength  in  short  blocks  of  about  2,000  pounds 
per  square  inch.  To  have  a  factor  of  safety  of  four,  as  it 
should  have,  a  compressive  unit  stress  or  an  extreme  fibre 
stress  in  beams  of  about  500  pounds  per  square  inch  should 
be  employed  in  the  design.  Concrete  in  short  blocks  can 
be  stressed  to  this  amount  with  safety.  It  is  therefore  a 
proper  unit  for  reinforced  concrete  columns  or  beams.  It 
would  not  be  safe  in  a  plain  concrete  column,  because  a 
plain  concrete  column  (having  a  length  several  times  its 
diameter),  will  fail  in  other  ways  than  in  direct  compres- 
sion, such  as  bulging  or  diagonal  shear.  But  where  the 
concrete  is  tied  together  by  steel  in  such  a  way  that  the 
concrete  is  not  subject  to  any  but  compressive  strains  in 
short  braced  elements,  failures  by  bulging  or  by  diagonal 
shear  are  prevented. 

Steel  buildings  are  commonly  built  in  lengths  of  several 
hundred  feet  without  expansion  joints,  depending  upon  the 
elasticity  of  the  steel  to  take  up  temperature  stresses.  Re- 
inforced concrete  builders,  essaying  to  do  the  same  thing 
with  the  less  elastic  materials,  are  apt  to  have  serious 
trouble.  If  a  long  wall  or  building  is  brought  up  from  one 
end  to  the  other,  so  that  the  shrinkage  of  the  concrete  does 
not  act  on  the  whole  line  at  once,  it  is  believed  that  one  or 
two  hundred  feet  of  continuous  reinforced  concrete  can 
be  maintained  in  one  piece.  The  placing  of  the  concrete 
should  be  done  from  one  end  to  the  other  of  a  long  struc- 
ture where  possible.  It  is  well  to  have  expansion  or  cleav- 
age joints  and  two  sets  of  columns  in  very  long  buildings. 
So-called  expansion  joints,  where  the  two  parts  of  the 
building  coming  together  are  not  independently  self  sus- 
taining are  worse  than  no  provision  whatever  for  expan- 
sion. Two  sets  of  girders  on  one  column  with  an  expan- 
sion joint  between  them  would  mean  the  concentration  of 
all  of  the  temperature  stresses  on  the  columns. 

It  is  very  important  that,  excepting  at  expansion  joints, 
structures  be  tied  together  continuously.  A  break  in  the 

262 


continuity  of  the  steel  results  in  a  weak  point  or  section  in 
the  structure  under  temperature  stresses. 

In  the  matter  of  the  time  allowed  for  the  setting  of  con- 
crete the  practice  common  with  plain  concrete  will  not 
apply  in  reinforced  concrete.  In  plain  concrete  the  forms 
can  often  be  removed  in  a  day  or  two  after  the  concrete 
has  been  placed,  and  no  harm  results.  This  is  because  the 
stresses  in  plain  concrete  are  not  of  the  intensity  of  those 
in  reinforced  concrete,  and  because  of  the  further  fact  that 
plain  concrete  seldom  receives  its  calculated  load  until  the 
structure  it  supports  has  been  built  up  over  it,  which  may 
be  months  later.  The  dead  weight  of  reinforced  concrete 
beams  and  slabs  is  a  large  part  of  the  total  load  which  they 
carry,  hence  they  should  not  be  called  upon  to  support  their 
own  weight  until  the  concrete  has  attained  the  greater  part 
of  its  calculated  strength.  In  a  current  engineering  periodi- 
cal, description  is  given  of  a  building  in  which  the  state- 
ment is  made  that  forms  were  removed  from  some  very 
large  girders  two  days  after  the  concrete  was  placed.  There 
is  absolutely  no  warrant  for  such  practice.  The  straining 
of  the  steel  rods  before  the  concrete  has  firmly  gripped 
them  is  a  proceeding  that  is  fraught  with  great  danger  to 
the  safety  of  the  structure.  No  wise  builder  would  submit 
to  his  structure  being  subjected  to  a  test  two  days  after 
the  concrete  had  been  placed.  It  is  just  as  absurd  to  re- 
move the  forms  at  so  early  a  date.  Two  weeks  of  good 
weather  should  be  allowed  before  forms  are  removed,  and 
two  weeks  more  should  elapse  before  any  test  is  made.  In 
freezing  weather  a  longer  period  should  be  allowed,  as 
the  setting  of  cement  is  retarded  and  sometimes  almost 
suspended  in  freezing  temperatures. 

If  construction  is  proceeding  upwards,  as  in  buildings, 
speed  should  not  be  too  great.  If  too  much  weight  is 
placed  upon  the  columns  while  the  concrete  is  green,  damage 
will  result.  Forms  for  concrete  columns  should  be  well  tied 
together  with  a  view  of  containing  the  semi-liquid  con- 
crete as  well  as  resisting  the  bursting  pressure  due  to  the 
load  that  may  come  upon  the  column.  Props  should  be 


placed  close  to  columns  as  well  as  under  intermediate  points 
in  the  beams  and  girders.  Column  forms,  as  usually  con- 
structed, are  not  suited  to  taking  vertical  loads,  but  are 
built  merely  as  boxes  to  contain  the  concrete.  The  cen- 
tering or  props  should  be  strong  enough  not  only  to  sup- 
port the  concrete  in  the  forms  immediately  above,  without 
sagging,  but  also  to  sustain  whatever  load  may  come  upon 
the  same  during  construction  for  the  time  that  it  takes 
the  concrete  to  set. 

The  qualities  that  make  the  combination  of  concrete  and 
steel  not  only  a  possibility,  but  also  a  means  of  meeting 
engineering  problems  that  in  many  ways  has  no  equal,  are 
these :  Concrete  and  steel  have  nearly  the  same  coefficient 
of  expansion  under  changes  of  temperature.  Concrete  in 
setting  in  the  air  will  shrink  and  grip  the  steel ;  it  will  also 
adhere  firmly  to  clean  or  somewhat  rusted  steel,  (but  not 
to  oily  steel).  Steel  imbedded  in  concrete  will  supply  the 
tensile  strength  that  the  concrete  lacks,  and  the  concrete 
will  preserve  the  steel  against  rust  besides  acting  as  a  pro- 
tection against  fire. 

That  the  coefficient  of  expansion  of  the  two  materials 
is  not  quite  the  same  is  reason  for  predominance  of  the 
weaker  material.  Large  sections  of  steel  in  comparatively 
small  sections  of  concrete  should  not  be  used,  as  the  ex- 
pansion and  contraction  of  the  steel  will  crack  the  con- 
crete. The  need  of  mass  in  the  concrete  to  grip  the  steel 
to  the  capacity  of  its  tensile  strength  is  another  reason  why 
the  steel  should  occupy  only  a  small  fraction  of  the  sec- 
tional area  of  a  beam  or  slab. 

The  placing  of  steel  directly  against  the  forms  and  thus 
allowing  it  to  be  on  the  surface  of  the  beam  or  slab  is  bad 
practice.  The  steel  is  by  this  means  exposed  to  fire  and 
rust,  and  it  cannot  be  effectually  gripped.  Steel  rods  should 
be  several  times  their  diameter  from  the  surface  of  the 
concrete.  Beams  narrow  at  the  bottom  and  wide  at  the 
top  are  irrational  in  shape.  They  lack  in  concrete  just 
where  it  is  needed  to  protect  and  grip  the  steel.  So-called 
T  beams,  which  are  rectangular  beams,  including  in  their 

264 


calculation  a  portion  of  the  floor  slab  as  top  flange,  are 
faulty  in  like  manner,  in  that  they  do  not  contain  enough 
concrete  in  the  lower  part  of  the  beam  for  the  amount  of 
steel  used. 

Floor  plates  in  steel  construction  are  not  considered  as 
adding  to  the  strength  of  floor  beams,  even  though  firmly 
riveted  thereto.  It  is  not  good  engineering  to  consider  a 
wide  expanse  of  floor  slab  as  part  of  a  narrow  beam,  and 
it  is  not  doing  justice  to  the  owner  to  make  a  floor  slab 
which  he  cannot  cut  into,  for  the  many  necessary  pur- 
poses that  openings  are  often  made  in  floors,  without 
weakening  the  primary  support  of  his  floor. 

Wide  flat  bars  bedded  in  concrete  are  not  held  as  firmly 
as  square  and  round  bars  of  the  same  sectional  area,  and 
are  not  suitable  shapes,  for  the  reason  that  the  concrete 
tends  to  shrink  away  from  the  flat  sides.  Flat  bars  have 
the  further  disadvantage  that  they  make  a  plane  of  cleav- 
age in  the  concrete.  This  is  especially  true  if  they  are  near 
the  surface.  The  writer  observed  some  reinforced  concrete 
beams  in  which  several  flat  bars  were  placed  side  by  side 
and  brought  up  and  hooked  over  the  steel  beams.  When 
the  forms  were  removed,  large  chunks  of  concrete  below 
the  flats  fell  off.  Square  and  round  rods  should  there- 
fore be  used  in  preference  to  flat  bars. 

The  writer  has  no  quarrel  with  mechanical  bond,  but  he 
believes  th'at  more  is  to  be  gained  by  use  of  plain  com- 
mercial steel  and  a  low  unit  tension  than  by  using  mechani- 
cal bond  and  the  high  unit  tension  advocated  by  those  who 
have  the  special  material  to  sell.  If  the  question  of  economy 
cuts  no  figure,  the  use  of  deformed  rods  under  low  unit 
stress  will  add  an  element  of  safety,  which  is  more  in  the 
nature  of  insurance  against  bad  work  in  the  execution  than 
a  needful  precaution  in  the  design. 

The  proper  use  of  the  steel  is  to  take  tensile  stresses. 
Composite  structures,  such  as  the  combination  of  wood  and 
iron  in  a  beam,  are  poor  makeshifts  at  the  best.  Where 
dissimilar  materials  are  used  to  perform  the  same  office 
jointly  there  is  no  correct  way  of  determining  just  how 

265 


much  of  the  work  each  will  do.  A  column  having  longitudi- 
nal sections  of  steel  that  are  intended  to  share  in  supporting 
the  load  is  a  composite  of  concrete  and  steel  and  not  a  true 
reinforced  concrete  column.  Calculations  to  determine  the 
relative  amounts  taken  by  the  steel  and  concrete  are  ren- 
dered useless  by  reason  of  the  tendency  of  the  concrete 
to  shrink  and  shorten. 

Segmental  floor  arches,  that  is,  arches  flat  on  top  and 
curved  upward  on  the  under  surface,  with  steel  reinforce- 
ment near  this  curved  surface,  violate  the  principles  of 
good  design.  If  these  act  as  arches  and  not  slabs,  they 
need  tie  rods  where  they  would  pierce  the  curved  surface 
and  be  unsightly  in  a  ceiling;  the  steel  is  in  compression 
in  place  of  tension.  If  they  act  as  slabs,  they  are  shallow 
and  weakest  where  they  should  have  the  greatest  strength. 

The  steel  in  reinforced  concrete  should  be  in  compara- 
tively small  sections,  well  distributed  through  the  mass. 
Not  only  should  there  be  the  steel  which  calculations  show 
to  be  required  for  tension,  but  it  is  very  often  desirable  to 
use  steel  rods  at  right  angles  to  the  primary  rods  in  order 
to  tie  the  concrete  together  and  prevent  cracking.  These 
cross  rods  also  aid  greatly  in  the  lateral  distribution  or 
spreading  of  concentrated  loads,  as  in  arches  or  slabs.  Wire 
mesh,  in  which  the  wires  are  straight,  is  an  excellent  ma- 
terial for  floor  slabs  of  small  span;  as  uniform  spacing  of 
the  steel  wires  is  assured,  and  they  are  not  easily  displaced 
in  placing  the  concrete. 

If  wires  or  rods  are  bent  or  kinked,  the  tendency  of  stress 
in  the  same  will  be  to  straighten  out  the  bends  and  kinks. 
This  means  excessive  stretch  in  the  steel  accompanied  by 
cracks  in  the  concrete.  The  use  of  wire  cables  is  irra- 
tional. It  is  a  well  known  fact  that  a  wire  cable  will  stretch 
several  times  as  much  as  a  steel  rod  of  the  same  sectional 
area  under  the  same  load.  The  principal  reason  for  using 
wire  cable  must  be  because  of  the  high  tensile  strength  of 
the  steel.  Now  if  a  high  unit  is  used  in  the  cable,  the 
stretch  will  be  still  further  augmented. 

Rods  imbedded  in  concrete  should  not  be  given  angular 

26G 


bends.  If  a  rod  under  stress  is  bent  at  an  angle,  there 
will  be  a  large  component  of  stress  at  the  bend  in  a  direc- 
tion bisecting  the  angle  between  the  portions  of  the  rod. 
There  is  evidently  nothing  at  the  bend  to  take  this  com- 
ponent but  a  small  area  of  concrete  bearing  on  the  rod  at 
the  bend.  The  use  of  sharp  bends  in  rods  is  a  very  com- 
mon fault  in  reinforced  concrete  design.  It  is  inexcusable. 
These  rods  should  be  given  gentle  curves,  so  that  the  side 
bearing  will  not  be  excessive.  If  we  allow  a  side  pressure 
on  the  concrete  one-twentieth  of  the  tensile  unit  on  the 
steel,  we  may  arrive  at  a  safe  minimum  radius  of  curva- 
ture of  a  rod  as  follows :  Let  d  =  diameter  of  a  square 
rod,  and  p  =  unit  pressure  allowed  on  the  concrete.  Then 
2Op  will  be  the  unit  tension  on  the  steel,  and  20  pd2  — 
stress  in  rod.  But  the  stress  in  the  rod  must  equal  the 
product  of  the  width  d  of  the  rod,  the  radius  of  curvature  r, 
and  the  unit  pressure  on  the  concrete;  or  20  pd2  =  d  r  p, 
whence  r  =  2od.  That  is,  the  radius  of  curvature  of  a 
square  rod  should  not  be  less  than  20  times  the  diameter  of 
the  rod.  The  same  rule  may  be  applied  to  the  case  of 
round  rods  without  important  error. 

Hooks  at  the  ends  of  rods  as  a  means  of  end  anchorage 
have  the  same  structural  fault  as  sharp  bends.  They  can- 
not anchor  a  rod  for  its  full  tensile  strength.  A  proper 
anchor  for  a  rod  requires  a  washer  plate  or  other  bearing 
part  having  a  surface  in  bearing  against  the  concrete  about 
twenty  times  the  area  of  the  rod. 

No  tension  on  the  concrete  should  be  allowed  in  the 
calculation  for  the  strength  of  beams  or  slabs.  The  ten- 
sile strength  of  concrete  is  uncertain  and  unreliable,  es- 
pecially where  it  may  be  subject  to  expansion  cracks  due 
to  the  presence  of  the  steel.  One  crack  in  a  beam  may 
destroy  entirely  an  assumed  tensile  value,  although  the 
same  crack  might  not  be  a  serious  matter  in  a  beam  not 
calculated  to  receive  any  assistance  from  the  tensile  strength 
of  the  concrete. 

The  allowed  tensile  unit  on  the  steel  is  a  feature  of  de- 
sign that  has  not  received  the  attention  that  it  merits.  The 

267 


mere  integrity  of  the  steel  under  a  given  tension  per  square 
inch  may  be  taken  care  of,  and  yet  the  stretching  out  of 
the  steel  under  that  stress  may  be  such  as  to  disintegrate 
the  concrete.  Cracks  begin  to  appear  in  the  concrete  after 
the  stress  in  the  steel  has  passed  about  ten  or  twelve  thous- 
and pounds  per  square  inch.  Units  of  about  these  amounts 
should  therefore  be  used.  The  use  of  high  tension  on  the 
steel  is  indefensible.  There  seems  to  be  a  prevailing  opinion 
and  it  is  held  by  many  men  who  ought  to  know  better,  that 
high  carbon  steel  or  steel  that  by  cold  rolling  or  other- 
wise is  made  to  have  a  high  elastic  limit  will  elongate  less 
under  stress  than  ordinary  structural  or  soft  steel.  This 
is  entirely  erroneous.  For  stresses  below  the  elastic  limit 
all  grades  of  steel  have  practically  the  same  modulus  of 
elasticity,  that  is,  they  will  all  stretch  out  a  given  amount 
under  a  given  unit  stress.  Beyond  the  elastic  limit  the  soft 
steels  will  elongate  more  before  breaking,  but  the  proper- 
ties of  steel  under  stresses  beyond  the  elastic  limit  have 
nothing  at  all  to  do  with  the  design  of  reinforced  concrete. 
The  writer  has  in  mind  a  case  where  an  architect  wished 
to  obtain  rods  having  an  elastic  limit  of  60,000  pounds  per 
square  inch,  so  that  he  could  use  20,000  pounds  in  his  de- 
sign ;  because  the  building  laws  allowed  him  to  use  a  factor 
of  safety  of  three  on  the  basis  of  the  elastic  limit.  In  an- 
other case  a  designer  used  32,000  pounds  per  square  inch 
for  dead  load  stress  on  the  steel.  (This  information  was 
given  in  the  defense  of  the  design  of  a  bridge  that  failed.) 
There  is  absolutely  no  warrant  for  the  use  of  such  high 
stress  upon  steel  confined  in  concrete.  One  advocate  of 
the  use  of  high  steel,  and  mechanical  bond,  makes  the  de- 
fense that  the  mechanical  bond  will  distribute  the  cracks ; 
thus  virtually  admitting  that  the  high  tension  he  advocates 
will  result  in  cracks  in  the  concrete.  Public  confidence  is 
not  obtained  by  any  such  admissions  or  practices. 

Shear  in  steel,  while  it  has  a  conspicuous  place  in  specifi- 
cations and  building  codes,  has  practically  no  meaning  in 
reinforced  concrete.    For  a  steel  rod  to  be  in  shear  to  the 
extent   of    12,000   pounds   per    square    inch,    as    sometimes 
268 


allowed,  there  would  be  a  pressure  on  the  side  of  the  rod 
which  no  concrete  could  stand.  If  we  imagine  a  bar  one 
inch  square  projecting  normally  out  of  a  vertical  concrete 
wall,  and  a  vertical  load  of  12,000  pounds  resting  on  this 
rod  where  it  projects,  we  have  the  absurd  proposition  which 
12,000  pounds  per  square  inch  shear  on  imbedded  steel 
represents.  We  do  not  measure  the  bearing  power  of  a 
nail  driven  in  wood  by  the  shearing  strength  of  the  metal, 
but  by  the  bearing  power  of  the  wood.  So  in  reinforced 
concrete  the  bearing  power  of  the  concrete  must  govern  if 
any  steel  is  to  be  considered  in  shear.  So-called  shear  bars, 
while  they  may  have  a  place  in  tying  the  concrete  of  a  beam 
together  generally,  do  not  perform  that  office  by  acting  in 
shear,  but  they  are  in  tension  tying  together  the  parts  of 
a  beam  into  which  they  extend. 

Reinforced  concrete  will  not  work  wonders.  The  ma- 
terials are  amenable  to  the  laws  of  nature,  including  the 
law  of  gravitation,  as  has  too  often  been  demonstrated, 
where  ignorant  or  careless  builders  have  attempted  its  use. 
Unscientific  and  misleading  tests  have  led  exploiters  to 
launch  into  the  field  of  reinforced  concrete  with  a  system 
and  little  or  no  engineering  knowledge,  and  the  recorded 
failures  are  the  fruit.  Prospective  builders  are  deluded 
with  the  idea  that  some  special  system  will  accomplish 
feats  with  steel  and  concrete  that  are  almost  magic  and 
that  defy  all  theory.  Some  of  these  designs  find  their  way 
into  books  treating  of  the  subject,  where  a  learner  ought 
to  expect  to  find  only  absolutely  reliable  information. 

Designers  in  this  new  construction  have  the  advantage 
of  access  to  the  knowledge  gained  by  experience  and  study 
in  steel  construction,  and  as  a  consequence  great  strides 
have  been  made.  Arch  spans  of  150  feet  or  more  and 
buildings  of  sixteen  stories  do  not  astonish  us  because  of 
familiarity  with  the  great  achievements  in  steel  structures. 
In  the  case  of  steel  a  more  or  less  gradual  development 
took  place.  The  design  of  steel  work  has  come  to  be 
largely  a  matter  of  following  certain  rules  embodied  in 
the  specifications,  and  other  principles  known  to  the  struc- 

269 


tural  designer;  and  to  the  extent  that  the  personal  equa- 
tion is  eliminated  by  these  rules  is  the  design  perfected. 
Common  sense  and  professional  judgment  sound  well,  but 
they  are  too  often  just  another  way  of  expressing  the  work- 
ing of  the  process  colloquially  known  as  skinning.  In  light 
steel  bridges  it  is  not  uncommon  to  see  principles  of  good 
engineeering  thrown  to  the  wind.  It  will  not  do  to  follow 
the  same  course  in  structures  of  the  permanence  of  those 
in  reinforced  concrete.  A  reinforced  concrete  structure 
with  no  better  provision  for  rigidity  than  the  average  high- 
way bridge  (put  up  with  no  disinterested  engineering  super- 
vision), will  very  soon  shake  itself  to  pieces.  The  high- 
way bridge  has  the  advantage  in  this  respect  because  of  the 
tougher  material  of  which  it  is  made. 

The  sooner  reinforced  concrete  design  is  reduced  to  rule, 
and  the  more  inclusive  the  rules,  the  better  for  the  preserva- 
tion of  life  and  property. 

In  the  matter  of  methods  of  calculating  the  strength  of 
beams  many  formulas  have  been  brought  out,  the  great 
part  of  which  are  very  complex.  Complex  formulas  are  not 
consistent  with  the  nature  of  the  materials  nor  with  the 
result  of  tests.  Complex  formulas  lead  to  errors,  not  only 
on  account  of  the  difficulty  of  applying  them,  but  because 
of  the  blind  way  which  they  are  generally  applied. 

By  assuming  the  neutral  axis  always  at  the  center  of 
depth  of  the  concrete  beam  and  compression  in  the  con- 
crete as  uniformly  varying  from  the  neutral  axis  up,  the 
formula  for  bending  moment,  as  well  as  its  derivation,  are 
rendered  very  simple.  The  first  of  these  two  assumptions 
is  quite  rational,  because  of  the  fact  that  tests  to  locate  the 
neutral  axis  of  beams  under  safe  loads  have  shown  that 
it  lies  very  close  to  the  middle  of  beam.  The  second  as- 
sumption is  equally  sound.  By  the  principle  of  the  equality 
of  tensile  and  the  compressive  stresses  in  a  beam,  if  500 
and  10,000  pounds  be  used  as  extreme  compressive  stress 
in  concrete  and  tension  on  steel  respectively,  it  can  be 
shown  by  a  simple  calculation  that  there  will  be  i%  per 
cent  of  steel  area  in  the  beam.  It  is  not  the  purpose  in 

270 


this  article  to  give  formulas,  but  to  lay  down  general 
principles. 

The  common  form  of  beam  has  one  or  more  rods  near 
the  bottom  from  end  to  end.  These  rods  receive  their 
stress  by  increments  from  the  concrete.  These  increments 
come  in  the  form  of  horizontal  shear  in  the  concrete,  being 
transformed  from  horizontal  shear  to  stress  in  the  rods  by 
the  medium  of  the  gripping  power  of  the  concrete.  As  the 
web  of  a  plate  girder  must  have  sufficient  shearing  strength 
in  any  given  length  to  take  the  flange  increment  in  that 
length,  so  there  must  be  section  enough  in  the  concrete 
beam  to  take  the  increment  of  the  flange  in  a  given  length. 
The  shear  on  the  concrete  in  a  horizontal  section  just  above 
the  rods  must  be  provided  for  in  section  in  the  beam.  This 
is  one  of  the  reasons  why  narrow  beams  and  beams  that 
are  lacking  in  concrete  in  the  lower  part  of  the  rectangle 
are  faulty.  If  the  gripping  power  of  the  concrete  is  mea- 
sured by  the  area  of  the  rod  in  contact  with  the  concrete, 
and  that  gripping  power  is  taxed  to  its  safe  capacity  in  any 
beam,  the  area  of  the  horizontal  section  in  the  beam  should 
be  equal  to  the  area  of  the  surface  of  the  rods.  This  means 
that  square  rods  should  be  placed  four  diameters  apart  and 
round  rods  3.1416  times  their  diameter  apart. 

As  intimated,  the  holding  power  of  concrete  on  a  rod  is 
measured  by  the  area  of  rod  in  contact.  This  cannot  ex- 
ceed, in  amount  per  square  inch,  the  shearing  strength  of 
the  concrete,  for  it  is  clear  that  a  prism  could  shear  out, 
taking  just  the  skin  of  concrete  adhering  to  the  rod.  The 
adhesion  and  shear  are  usually  taken  at  about  the  same 
unit  value.  A  safe  amount  is  50  pounds  per  square  inch  for 
stone  concrete.  It  will  be  seen  by  a  little  calculation  that,  if 
a  rod  is  imbedded  fifty  diameters  in  concrete,  at  this  amount 
per  square  inch  of  its  surface,  it  will  be  anchored  to  the 
extent  of  10,000  Ibs.  per  square  inch.  Hence,  any  plain  rod 
not  anchored  with  nut  and  washer  at  the  end  must  be  im- 
bedded fifty  diameters  before  it  is  held  by  the  concrete  to 
the  amount  of  its  safe  capacity.  In  the  case  of  a  beam, 
however,  while  the  anchoring  value  increases  uniformly  to 

271 


the  center  of  the  span  the  stress  increases  as  the  ordinates 
of  a  parabola.  Hence,  in  order  to  have  the  anchoring  value 
not  less  than  the  stress  at  any  section  the  rod  should  have 
double  its  safe  anchoring  strength  at  the  center  of  span, 
since  the  tangent  to  the  parabola  at  the  ends  of  beam  cuts 
a  point  twice  as  high  as  the  middle  ordinate  at  the  center 
of  span.  This  would  require  100  diameters  up  to  the  cen- 
ter of  span.  In  other  words  a  rod  not  anchored  at  the 
end  of  span,  or  continuous  into  the  next  span  should  not 
exceed  in  diameter  one  two-hundredth  of  the  span. 

The  curving  of  a  rod  up  to  the  top  flange  at  the  ends 
of  span,  without  providing  an  end  anchorage  or  running 
the  rod  into  the  adjacent  span  for  anchorage,  is  another 
structural  fault,  and  a  common  one.  This  takes  the  rod 
out  of  the  plane  where  flange  increments  are  added  (near 
the  bottom  of  the  beam)  and  makes  a  suspension  rod 
of  it  on  which  the  concrete  rests  as  a  saddle.  It  is  neces- 
sary in  such  a  case  that  nearly  the  full  stress  of  the  rod 
should  be  imparted  to  it  at  the  very  end,  where  in  many 
designs  there  is  absolutely  nothing  to  perform  this  office. 
If  a  rod  curved  up  at  the  end  of  one  beam  runs  beyond 
the  support  into  an  adjacent  beam,  it  serves  the  double 
purpose  of  anchoring  the  rod  and  taking  tension  in  the 
top  flange  of  the  next  beam  that  would  be  caused  by  the 
continuity  of  the  beams  over  the  support.  Separate  rods 
lying  near  the  top  of  beams,  where  two  beams  occur 
end  to  end  over  the  same  support,  are  of  great  value  in 
resisting  negative  moments  over  supports,  and  should 
be  made  use  of  in  the  absence  of  the  arrangement  just 
mentioned  (where  the  bottom  rods  of  one  span  continue 
into  the  next  to  resist  tension  in  the  top  flange).  These 
separate  rods  should  extend  not  less  than  50  diameters 
into  each  beam  for  anchorage,  and  may  require  to  be 
longer.  Rods  running  from  one  beam  into  the  next 
for  anchorage  should  extend  into  that  beam  not  less 
than  50  diameters. 

In    steel    work   beams    are   not    usually    considered    as 
continuous,  unless  it  be  necessary  to  take  care  of  canfi- 
272 


lever  stresses,  but  in  steel  beams  there  is  ample  strength 
in  the  top  flange  to  take  care  of  any  tension  that"'  may 
occur  due  to  continuity.  With  reinforced  concrete  beams 
the  case  is  quite  different.  Where  two  beams  in  a  line 
resting  on  the  same  support  are  poured  at  once,  there 
will  be  sure  to  be  some  tension  in  the  top  flange;  and 
if  this  is  not  resisted  by  steel,  a  crack  may  be  the  result, 
which  would  destroy  the  shearing  strength  of  the  con- 
crete, and  might  cause  the  beam  to  fail  by  shear. 

The  end  shear  of  a  reinforced  concrete  beam  or  slab 
with  only  horizontal  rods  must  be  taken  by  the  con- 
crete. When  a  beam  of  a  given  span  is  increased  in 
depth,  the  bending  strength  and  consequently  the  capacity 
for  load  is  increased  about  as  the  square  of  the  depth. 
The  shearing  strength  is,  however,  only  increased  as 
the  depth.  There  will  therefore  be  a  point  where  the 
shearing  value  is  overtaxed,  and  beyond  which  the  depth 
should  not  be  increased  without  some  provision  for  taking 
the  extra  shear.  In  a  subsequent  article  the  writer  hopes 
to  show  that  this  limiting  depth  is  one-tenth  of  the  span. 
When  the  depth  of  beam  is  more  than  one-tenth  of  the 
span,  some  provision  must  be  made  for  taking  the  shear 
that  the  concrete  is  not  capable  of  carrying.  The  mere 
turning  up  of  some  rods  and  ending  them  short  of  the 
end  of  span,  or  running  them  to  the  end  of  span  without 
anchorage  at  the  end  of  span,  will  not  do  this. 

For  columns  a  circular  coil  to  resist  the  bursting  or 
bulging  pressure  and  longitudinal  rods  tied  to  this  coil 
at  regular  intervals  in  the  circle  to  resist  flexure,  seems 
to  be  the  most  rational  means  of  overcoming  the  weak- 
nesses of  concrete  as  a  column. 


273 


The  Design  of  Reinforced  Concrete 
Beams  and  Slabs. 

Based  on  the  principles  of  design  laid  down  by  the 
writer  in  an  article  published  in  Concrete  Engineering 
of  January  I,  1907,  the  following  is  given  as  exemplifying 
simplified,  and  at  the  same  time  rational  design  as  ap- 
plied to  beams  and  slabs  in  reinforced  concrete. 

There  are  two  ways  of  finding  the  safe  strength  of  a 
beam  or  slab,  one  is  to  use  in  the  formula  ultimate 
values  and  then  apply  a  factor  of  safety;  the  other  is  to 
use  in  the  formula  safe  values,  thus  applying  the  factor 
of  safety  before  the  formula  for  strength  is  reached. 
These  two  methods  should  not  be  divorced  from  each 
other,  but  their  interdependence  should  be  recognized. 
Stresses  that  would  be  quite  safe  for  steel  in  a  framed 
structure  may  be  unsafe  in  steel  imbedded  in  concrete, 
by  reason  of  the  excessive  stretch  and  the  consequent 
cracking  of  the  concrete.  And  again  there  should  be 
some  approximate  agreement  between  the  ultimate  strength 
of  beams  as  shown  in  the  formula  and  the  ultimate 
strength  of  test  beams  as  found  by  experiment.  Formulae 
to  be  of  value,  must  be  based  upon  assumption  of  the 
continued  elasticity  of  the  materials  up  to  the  point  of 
failure,  and  for  this  reason  exact  agreement  between 
the  calculated  ultimate  strength  and  that  shown  in  tests 
is  not  to  be  expected,  In  fact  the  variation  in  the  strength 
of  concrete  would  preclude  any  such  exact  agreement. 

The  ultimate  usefulness  of  steel  is  reached  when  the 
material  is  stressed  to  its  elastic  limit,  or  say  40,000 
pounds  per  square  inch,  which  is  about  the  elastic  limit, 
as  shown  by  drop  of  beam,  for  the  vast  majority  of  tests 
commercially  made  on  structural  steel.  High  steel  is 
not  considered  in  this  connection,  for  its  use  is  neither 
appropriate  nor  economical.  At  this  value  for  the  stress 
in  steel  cracks  are  sure  to  be  plainly  visible  and  bond 
between  the  concrete  and  steel  is  greatly  weakened,  if 
not  destroyed.  Using  40,000  pounds  per  square  inch  as 

1174 


the  ultimate  tensile  value  and  a  factor  of  safety  of  four 
for  rolling  loads,  such  as  those  on  floors  where  wheeling 
is  done,  or  in  bridges,  we  have  10,000  pounds  per  square 
inch  as  the  safe  limit  on  the  steel.  It  is  safe  to  say  that 
if  the  stress  on  the  steel  be  kept  within  this  limit,  other 
parts  of  the  design  being  equally  well  proportioned,  the 
integrity  of  the  structure  will  be  completely  safeguarded. 

Unlike  steel,  concrete  is  elastic  practically  up  to  the 
point  of  failure.  Good  stone  concrete,  of  the  proportions 
of  I  volume  of  Portland  cement  to  2  of  sand  and  4 
of  hard  broken  stone,  will  show  in  short  blocks  an  ulti- 
mate strength  of  about  2,000  pounds  per  square  inch 
after  setting  several  months.  This  may  then  be  taken 
as  the  ultimate  strength  of  concrete  in  beams,  and  on 
the  same  basis  as  the  steel  the  safe  value  is  500  pounds 
per  square  inch.  The  ratio  then  between  the  unit  stress 
in  the  steel  and  the  extreme  fibre  stress  in  the  concrete 
is  20. 

By  the  well-known  principle  of  the  equality  of  tensile 
and  compressive  stresses  in  a  beam  subject  to  bending 
only  we  know  that  the  total  tension  in  the  steel  must 
equal  the  total  compression  in  the  concrete.  As  stated 
in  the  article  previously  referred  to,  no  tension  will  be 
counted  upon  as  existing  in  the  concrete.  The  variation 
of  stress  in  the  concrete  will  be  taken  as  uniform  from 
the  neutral  axis  up,  and  the  neutral  axis  will  be  taken 
as  located  in  the  middle  of  the  depth  of  the  concrete 
beam  or  slab. 

Let  D  =  depth  in  inches  of  concrete  beam  or  slab  out 
to  out;  B— width  of  beam  in  inches;  A= area  of  steel 
in  square  inches;  M— ultimate  bending  moment  in  inch- 
pounds  on  beam  AB ;  M'—  bending  moment  in  foot 
pounds  on  beam  or  slab  one  foot  in  width. 

The  ultimate  stress  in  concrete  is  2, oooX^ D^tyB— 
500  BD.  This  must  equal  the  stress  in  the  steel  or  40,000 
A.  Hence  A=i-So  of  BD  or  1.25  per  cent,  of  the  area 
of  the  concrete  rectangle. 

The  center  of  gravity  of  the  stress  in  the  concrete  is 

275 


one-third  of  D  above  the  neutral  axis,  and,  if  we  place 
the  steel  one-eighth  of  D  from  the  bottom  of  concrete, 
it  will  be  three-eighths  of  D  below  the  neutral  axis.  The 
effective  depth  is  then  17-24  D,  and  the  ultimate  bending 
moment  is 

M  =  17-240  X  SooBD  =  354BD2 

If  a  beam  or  slab  12  inches  wide  be  considered,  the 
ultimate  bending  moment  on  the  same  in  foot-pounds 
will  be 

M'  =  1-12  X  354  X   I2E)2  =  354D2 
Allowing  a   factor  of   safety   of  four   for  rolling  loads 
and   3.5    for    quiescent    loads    we   have    for    safe   bending 
moment  per  foot  width 

M'  for  rolling  loads  =  88D2  (i) 
M'  for  quiescent  loads  =  ioiD2  (2) 

By  the  same  process  we  may  derive  the  following  for 
steel  placed  one-sixth  of  the  depth  from  bottom  of 
concrete 

M'  for  rolling  loads  =  SsD2  (3) 
M'  for  quiescent  loads  —  Q5D2  (4) 

For  steel  placed  one-tenth  of  the  depth  the  safe  bend- 
ing moment  per  foot  width  is 

M'  for  rolling  loads  =  Q2D2  (5) 
M'  for  quiescent  loads  =  iosD2  (6) 

The  foregoing  considers  only  the  bending  moment  in 
the  beam  or  slab,  and  deals  only  with  the  amount  and 
location  of  steel  to  reinforce  a  concrete  beam  for  a  given 
bending  moment.  In  all  beams  shear  plays  an  important 
part  and  must  be  taken  care  of.  In  steel  beams  this  office 
is  performed  by  the  web  plate.  In  reinforced  concrete 
beams  provision  for  gripping  the  rods  must  be  made. 
This  corresponds  in  structural  steel  design  to  the  spac- 
ing of  rivets  in  the  flange  to  take  the  flange  increment. 

Some  of  the  rules  laid  down  in  the  writer's  previous 
article  are  these: 

(a)  The  diameter  of  horizontal  straight  rods  not  an- 
chored at  the  ends  of  span  should  not  exceed  1-200  of 
the  span. 

276 


(b)  The  spacing  of  rods  in  which  the  gripping  value 
is  taxed  to  the  safe  limit  (as  where  the  diameter  is  1-200 
of  the  span)  should  be  four  diameters  for  square  rods 
and  3.1416  diameters  for  round  rods. 

Coupled  with  the  latter  rule  it  is  to  be  observed  that 
the  distance  from  center  of  outside  rod  to  edge  of  beam 
should  be  one-half  of  the  spacing.  This  is  so  that  the 
shearing  area  in  a  plane  just  above  the  rods  will  be 
equal  to  the  superficial  area  of  the  rods.  If  rods  of  less 
diameter  than  1-200  of  the  span  are  used,  the  gripping 
value  is  not  taxed  to  its  safe  limit.  In  such  case  the 
spacing  can  be  closer.  The  area  of  the  horizontal  section 
of  the  beam  should  be  not  less  than  the  superficial  area 
of  the  rods  in  a  length  of  200  diameters,  for  beams  taking 
uniform  loads. 

Rods  should  be  several  times  their  diameter  from  the 
bottom  of  the  beam,  so  as  to  make  the  gripping  of  con- 
crete effective.  With  1.25  per  cent,  of  steel  and  round 
or  square  rods  spaced  3.1416  and  4  times  their  diameters 
apart  respectively,  rods  %  of  D  from  the  bottom  of  con- 
crete, it  will  be  found  that  the  center  of  rod  is  2%  diame- 
ters from  the  bottom  of  the  concrete  beam.  This  is  in 
good  proportion. 

By  rules  (a)  and  (b)  the  gripping  of  rods  and  the 
increment  to  the  stress  in  rods,  as  well  as  the  horizontal 
shearing  strength  of  the  beam,  are  taken  care  of. 

For  vertical  shear,  with  only  horizontal  rods,  the  end 
shear  must  be  taken  by  the  rectangle  of  concrete  having 
sides  B  and  D.  It  is  a  well  known  principle  of  mechanics 
that  the  intensity  of  shear  in  a  rectangular  beam  varies 
as  the  ordinates  of  a  parabola,  being  a  maximum  at  the 
middle  of  the  depth  of  rectangle,  where  it  is  three-halves 
of  the  average. 

Concrete  in  shear  partakes  of  the  weakness  of  concrete 
in  tension,  because  it  depends  for  its  value  to  a  large 
extent  on  the  tenacity  of  the  material.  In  simple  com- 
pression a  loose  hard  material,  such  as  sand,  if  it  be 
confined,  has  great  strength,  but  it  can  have  no  shearing 

277 


strength.  Reinforcement  confines  concrete  to  a  large  de- 
gree, and  lessens  dependence  upon  tenacity  in  the  material 
itself.  Concrete  in  compression  can  therefore  have  a 
much  greater  relative  safe  value  than  in  shear.  Shear 
must  be  depended  upon  in  design,  but  its  unit  value 
should  be  low.  If  50  pounds  per  square  inch  be  taken  as  a 
safe  limit  in  shear,  the  average  on  the  rectangle  should 
be  two-thirds  of  this.  The  allowed  end  shear  is  then 
shown  by  the  following  equation 

W 

—  =   12  D  X  2-3  X  50,  or  W  =  800  D 

2 

where  W  is  the  total  load  in  pounds  on  a  beam  or  slab 
12  inches  wide. 

The  bending  moment  in  a  uniformly  loaded  beam,  car- 
rying a  total  load  W  is  W  times  VB  of  the  span.  If  L  = 
span  in  feet  we  have,  from  (i) 

L 
M'  —  88D2  =  8ooD  x  —  =  iooDL 

^j*l  8 

or  88D=:iooL,  and  since  D  is  in  inches  and  L  in  feet, 

the  actual  ratio  of  D  to  L  is  about  I  to  10.  Hence,  when 
the  depth  of  a  beam  or  slab  is  greater  than  one-tenth  of 
the  span,  the  concrete  is  overtaxed  in  shear,  and  must  be 
reinforced. 

This  reinforcement  is  best  effected  by  curving  up  some 
of  the  rods  and  anchoring  them  at  the  ends  or  passing 
them  over  into  adjacent  spans. 

By  an  arrangement  such  as  shown  in  Fig.  i  the  total 
end  shear  is  taken  by  the  rod,  at  least  such  of  the  shear 
as  is  represented  by  the  load  giving  the  stress  in  the  rod 
that  is  curved  up.  If  some  of  the  rods  are  curved  up 
and  anchored  at  the  ends  of  span  and  others  are  horizontal 
throughout,  the  concrete  will  be  called  upon  to  take  only 
the  end  shear  represented  by  the  part  of  the  load  taken 
by  the  horizontal  rods. 

Continuous  beams  are  of  frequent  occurrence  in  rein- 
forced concrete  being  almost  a  necessary  result  of  the 

278 


00 

rio 


2 

W 
^ 
< 


Q 
15 

W 
J 

< 

s 

H 

K 


O 

.—  j 

/  -1 

/> 

V 

l 

279 


nature  of  its  manufacture.  The  bending  moment  on  an 
indefinite  line  of  continuous  beams  all  uniformly  loaded, 
or  that  on  a  fixed  ended  beam,  is  two-thirds  of  that  of  a 
simple  beam.  This  moment  is  negative  and  occurs  at  the 
supports;  at  the  center  of  one  of  these  beams  the  bend- 
ing moment  is  less,  but,  if  the  adjacent  beams  be  relieved 
of  their  live  load,  the  bending  moment  at  the  center  of 
this  beam  increases  to  an  amount  depending  upon  the 
relation  between  dead  and  live  load.  For  these  reasons 
some  designers  use  two-thirds  of  the  simple  beam  mo- 
ment for  reinforcement  at  center  and  ends  of  beams  that 
are  continuous.  There  are  several  objections  to  this. 
First,  the  formula  for  continuous  beams  is  based  on  beams 
having  a  uniform  moment  of  inertia.  This  is  not  true  of 
reinforced  concrete  beams.  Second,  it  is  generally  im- 
practicable to  make  the  last  beam  of  a  line  fixed  at  the 
end,  and  the  bending  moment  of  a  beam  of  uniform  mo- 
ment of  inertia,  fixed  at  one  end  and  simply  supported 
at  the  other,  is  equal  to  that  of  a  beam  simply  supported 
at  both  ends.  This  bending  moment  is,  however,  at  the 
fixed  support  and  is  negative.  In  a  continuous  beam  the 
moment  at  this  support  may  exceed  two-thirds  of  that 
of  a  simple  beam.  Third,  uniform  load  on  all  spans  does 
not  give  the  maximum  moment  at  the  middle  of  a  span. 
Fourth,  the  relief  moment  at  the  supports  in  any  beam 
under  consideration,  assuming  that  beam  to  be  fully 
loaded  and  the  side  beams  unloaded,  is  at  the  expense 
of  negative  moments  in  the  side  beams,  which  may  re- 
quire reinforcement  in  the  top  of  beams  throughout  their 
length.  Complete  reinforcement  at  top  and  bottom  of 
beams  throughout  the  span  is  not  desirable  and  is  not 
economical.  Fifth,  some  beams  in  the  structure  may  not 
be  joined  end  to  end  with  other  beams,  and  some  may 
not  be  of  the  same  span  as  those  adjacent.  Complications 
would  thus  be  introduced  that  no  simple  rule  would 
cover.  Sixth,  in  alterations  on  the  structure  a  beam 
may  be  taken  out  upon  which  another  depends  for  its 

280 


strength.  Seventh,  unequal  settlement  of  supports  will 
disturb  the  condition  of  assumed  continuity. 

The  first  reason  given  above  is  sufficient  to  condemn 
the  use  of  the  purely  theoretical  method,  not  because  the 
theory  itself  is  incorrect,  but  because  it  is  not  applicable. 
Fully  carried  out  the  theory  of  the  continuous  beam 
would  greatly  complicate  both  the  design  and  the  execu- 
tion, and  it  would  not  possess  the  redeeming  feature  of 
being  correct.  A  further  reason  why  top  reinforcement 
as  a  primary  element  of  strength  should  be  avoided 
where  practicable  is  this  practical  one.  In  a  fire  the  prin- 
cipal damage  to  floors  is  on  the  under  side  where  heat  is 
greatest,  and  is  usually,  in  the  case  of  concrete,  of  the 
nature  of  spalling  at  the  surface.  Damage  to  the  con- 
crete of  a  beam  or  slab  on  the  tension  side  affects  only 
the  grip  on  the  steel,  and  would  have  to  be  extensive  to 
be  serious;  whereas  a  small  amount  of  spalling  on  the 
compression  side  would  greatly  weaken  a  reinforced  con- 
crete beam. 

If  each  beam  be  reinforced  for  its  full  bending  moment 
as  a  simple  span  in  the  way  outlined  above,  there  can  be 
no  question  as  to  its  safety,  provided  the  top  flange  stress 
near  the  support  is  not  such  as  to  crack  the  concrete  and 
thus  weaken  the  beam  in  shear.  There  remains,  then, 
the  necessity,  in  beams  where  continuity  exists,  of  pre- 
venting tension  in  the  concrete  "in  this  portion  of  the  beam. 
The  rigidity  of  the  beam,  if  fully  reinforced  for  the 
simple  beam  moment,  will  be  greater  than  if  reinforced 
for  only  a  part  of  that  moment,  and  the  deflection  will 
be  less.  Hence  the  tendency  to  produce  tension  in  the 
top  flange  near  the  supports  is  diminished.  To  overcome 
this  tendency  it  is  recommended  that  reinforcement  be 
used  to  the  amount  of  one-half  of  that  at  the  center  of 
beam  and  that  the  reinforcing  rods  extend  at  least  through 
one-quarter  of  the  span.  This  would  be  equivalent  in 
total  reinforcement  to  three-quarters  of  the  full  rein- 
forcement at  center  of  span  and  three-quarters  at  sup- 
ports, and  would  be  distributed  in  a  more  rational  manner. 

281 


In  an  arrangement  such  as  shown  in  Fig.  2,  if  the  upper 
rod  is  made  continuous  and  horizontal  near  ends  of  span 
for  a  portion  of  the  span,  as  indicated,  the  tension  in  the 
upper  part  of  the  beam  at  supports  will  be  taken  care  of. 
Tension  in  these  rods,  however,  in  the  curves  at  A  gives 
a  force  in  the  direction  of  the  arrows,  causing  tension  in 
the  bottom  of  beam.  In  such  case  the  bottom  rod  should 
also  be  continuous  or  else  anchored  at  supports,  as  there 
is  a  tension  under  the  arrows,  where  these  rods  would 
have  developed  only  a  portion  of  their  anchorage,  if  not 
secured  at  the  ends  of  span.  With  rods  so  arranged  in 
continuous  beams  one-half  of  the  reinforcing  rods  may 
be  brought  up  near  the  top  flange  over  supports  and  the 
other  half  made  horizontal  throughout.  Splicing  of  rods 
should  be  over  supports,  either  with  sleeve  nuts,  which 
is  preferable,  or  by  lapping  rods  fifty  diameters.  The 
continuity  of  bottom  rods,  as  well  as  top  rods,  adds 
greatly  to  the  rigidity  of  the  building. 

In  the  case  of  slabs  of  short  span  there  is  scarcely  any 
need  of  reinforcement  near  the  top  of  slabs  over  sup- 
ports, because  of  the  extra  concrete  that  is  generally  pres- 
ent. The  concrete  supplies  a  rigidity  that  does  not  allow 
of  much  deflection,  and  the  danger  of  cracking,  if  the 
slab  is  properly  reinforced  near  the  bottom,  is  small.  The 
writer  made  some  tests  on  concrete  slabs  3  feet  8  inches 
in  clear  between  the  beams  and  3  inches  thick,  in  which 
there  was  no  reinforcement  whatever.  Many  of  these 
were  cracked  through  the  middle  parallel  to  beams.  In 
spite  of  the  cracks  and  the  absence  of  reinforcement  the 
slabs  showed  no  signs  of  distress  under  250  Ib.  per  square 
foot  of  superimposed  load.  Slabs  of  this  sort  should  un- 
doubtedly be  reinforced,  but  owing  to  the  excess  of  con- 
crete made  necessary  by  practical  considerations  of  thick- 
ness, the  rigidity  resulting  therefrom  is  warrant  for  the 
omission  of  top  flange  reinforcement. 

Continuous  slabs  of  long  span  deflecting  as  simple 
beams  would  bend  at  sharper  angles  over  the  support 
than  short  span  slabs.  Hence  the  need  of  top  flange  rein- 

282 


forcement  in  longer  spans.  Slabs  in  which  there  is  not 
an  excess  of  concrete  over  the  requirements  for  compres- 
sion will  not  be  as  rigid  as  those  in  which  there  is  an 
excess  of  concrete.  It  is  recommended  that  in  slabs  of  a 
span  of  9  feet  or  more,  and  in  all  cases  where  there  is 
an  area  of  three-quarters  of  one  per  cent  or  more  of 
steel,  one-half  of  the  reinforcing  rods  be  curved  up  over 
supports,  as  indicated  in  Fig.  2. 

As  an  example  of  the  application  of  the  foregoing  in 
the  design  of  the  floors  of  a  building,  given  a  building 
having  columns  15  feet  apart,  to  be  designed  for  a  live 
load  of  100  pounds  per  square  foot,  assumed  to  be  quies- 
cent. Assume  girders  between  columns  and  the  beams 
supported  by  the  same  to  be  spaced  5  feet  apart.  For 
the  floor  slab  assume  a  depth  of  3  inches.  By  equation 
(4)  the  bending  moment  per  foot  of  width  is  855  ft-lb. 
The  dead  load  in  this  case  is  40  Ib.  and  the  live  load 
100  Ib.  per  sq.  ft.  The  total  moment  is  then  140X25-^-8— 
438  ft.-lb.  The  area  of  steel  reinforcement,  instead  of 
being  1^4  per  cent  of  12x3  sq.  in.  (or  .45  sq.  in.)  will  need  to 
be  only  438/855  of  .45  or  .23  sq.  in.  per  ft.  width  of  slab. 
This  can  be  made  up  of  J4-in.  square  rods  spaced  3  in.  apart. 
These  should  be  placed  with  centers  ^  in.  above  the  bot- 
tom of  slab.  In  addition  there  should  be  say  two  rods 
running  parallel  to  the  beam  to  tie  the  concrete  together 
in  that  direction. 

For  the  beams  the  span  is  15  feet.  The  slab  weighs 
200  Ib.  per  ft.  of  beam;  the  assumed  weight  of  beam  in 
addition  is  130  Ib.  per  ft.  The  total  load  is  then  830  Ib. 
per  ft.  and  the  bending  moment  is 

830  X  i52-^8  =  2340oft.lb. 
Assuming  a  depth  of  18  in.  we  have  by  equation  (2) 

M'  per  foot  width  of  beam  =  101  X  i82  —  32700  ft.-lb. 
The  width  of  beam  is  then  23,400  -~  32,700  =  .716  ft.  or 
say  8^2  in.  For  reinforcement  i%  per  cent  of  18  X  &/^ 
=  1.9  sq.  in.  The  allowed  diameter  of  rods  is  1-200  of 
180  in.,  or  .9  in.  Three  round  rods  of  this  diameter  would 
make  up  the  exact  area  required.  Further,  the  circum- 


ference  of  the  three  rods  would  just  about  equal  the 
width  of  the  beam.  The  nearest  commercial  sizes  to  this 
are  %-in.  and  I5~i6-in.  For  the  purpose  of  having  an  even 
number  of  rods  four  round  rods  i3-i6-in.  in  diameter 
will  be  used.  The  superficial  area  of  these  rods  in  200 
diameters,  (—  162.5  in.)  is  1,658  sq.  in.;  the  area  of  a 
horizontal  section  of  the  beam  is  SVz  X  180  =  1,530; 
but  as  these  rods  are  of  larger  diameter  than  necessary, 
the  horizontal  shear  would  be  taken  care  of  in  this  beam 
if  all  rods  were  horizontal.  To  take  the  stresses  due  to 
continuity  two  of  these  rods  will  be  curved  up  at  sup- 
ports, as  shown  in  Fig.  2.  At  center  of  span  all  rods 
will  be  2^4  -in.  from  bottom  of  beam. 

For  the  girder  assume  a  depth  of  24  in.,  including  the 
depth  of  slab.  The  total  dead  weight  of  bay  is  about  19,000 
lb.,  and  the  live  load  carried  is  22,500  lb.,  a  total  of 
41,500  lb. 

When  a  girder  carries  beams  equally  spaced,  two  of 
which  are  at  the  ends  of  span,  the  bending  moment  is 
the  same  as  though  the  load  were  uniformly  distributed, 
if  one  of  these  beams  is  at  the  center  of  span,  that  is,  if 
there  is  an  even  number  of  spaces.  If  W  =  the  total  load, 
L=  span  in  feet,  the  bending  moment  =WL  -~  8.  If 
there  is  an  odd  number  of  spaces,  the  bending  moment 
is  less  by  the  value  of  the  moment  that  would  occur  in 
a  span  equal  to  the  space  between  beams.  For  example, 
if  there  are  five  spaces,  the  bending  moment  in  a  span 
L  W  L  WL 

-T-  is  ^~X""-|-^=:~^  ' 


WL_WL    3  W  L 

8         200  ~~     25 

In   the   present   case   there    are   three    spaces,    and   the 
bending  moment  is 

WL     WL     WL 

8   ~~  9x8  ~     9 
The  bending  moment  on  this  girder  is  then 


284 


/ 

I' 

j 

to 

\ 

•\ 

Vj 

» 

^ 

i 

p 

B 

>v 

5; 

$ 

^Q 

S 

/ 

( 

— 

^ 

! 

! 

i 

-*-  i 

41 

r-  "i 

p 

1 

Vi 

i 

I 

:  \ 
i  \ 

i! 
1*. 

r 

ft 
|fl 

\  ^  ^ 
|l^ 

\ 

^  ^ 

^/V^  / 

!S 

2l3a 

By  equation  (6)  M'  —  IO5D2  —  105  X  242  =  60480 
ft.-lb.  per  ft.  width  of  beam.  'The  beam  should  then  be 
14  in.  wide.  The  area  of  steel  required  is  I1/*  per  cent 
of  14  X  24  =  4.2  sq.  in.  This*may  be  made  up  of  seven 
%-in.  round  rods,  five  of  which  lie  horizontal  and  two  of 
which  are  curved  up  as  in  Fig.  i.  In  addition  to  these 
two  %-in.  rods,  which  pass  into  adjacent  beams  to  take 

i  the  stress  due  to  continuity,  there  can  be  two  %-in.  round 
rods  8  ft.  long  placed  near  the  top  of  girders  over  the 
support,  to  make  up  the  remainder  of  the  50  per  cent 

i    of  steel  area. 

The  end  shear  of  this  girder  is  about  one-third  of  the 
load  of  a  bay  or  14,000  lb.,  as  the  load  of  one  beam  is 
taken  directly  to  the  column.  At  a  nominal  ultimate  of 
200  lb.  per  sq.  in.  on  concrete  in  shear,  with  a  factor  of 
safety  of  3^2,  the  allowed  unit  is  57  lb.  per  sq.  in.  Two- 
thirds  of  this  as  the  average  on  the  rectangle  =  38  lb. 
per  sq.  in.  This  on  a  section  24  in.  x  14  in.  gives  12,800 
as  the  shear  allowed  on  the  concrete.  As  the  concrete 
is  called  upon  to  take  only  5-7  of  the  shear  the  shearing 
strength  is  ample.  At  center  of  span  all  rods  will  be  2.4 
in.  from  bottom  of  beam  (say  2%  in.).  The  five  horizontal 
rods  a're  to  be  equally  spaced,  being  2^4  in-  center  to 
center,  the  outside  ones  being  \Vz  in.  from  the  surface. 
The  two  curved  rods  may  lie  between  horizontal  rods. 
Fig.  3  illustrates  this  floor. 

Reinforced  concrete  lends  itself  to  construction  in  the 
form  of  slabs  supported  on  four  sides,  and  such  construc- 
tion may  in  some  cases  be  more  economical  than  the 
ordinary  beam  and  slab  design.  Given  a  square  slab  sup- 
ported on  all  four  edges,  the  side  of  the  square  being  L 
feet,  as  shown  in  Fig.  4.  Assume  that  this  slab  is  to  be 
reinforced  in  two  directions  at  right  angles  to  each 
other.  It  is  clear  that  the  strip  A  B,  i  ft.  wide,  and  the 
strip  /  each  being  similarly  placed  in  the  structure  will 
each  sustain  the  same  load.  Each  will  then  take  one-half 
of  the  load  on  the  middle  square  foot  of  the  slab.  The 
strips  2,  3,  4,  etc.,  will  be  prevented  from  deflecting  as  much 

286 


as  strip  I  and  hence  will  take  less  load  than  strip  I  in  pro- 
portion as  their  deflection  is  less.  Strip  A  B  will  then  be 
compelled  to  carry  more  than  half  of  the  load  on  the 
square  at  the  intersection  of  itself  and  strip  2  and  still 
more  at  the  intersection  with  strip  3,  etc.  It  is  sufficiently 
accurate  to  assume  that  the  deflections  of  strips  I,  2,  3,  4, 
etc.,  diminish  as  the  ordinates  of  a  parabola.  Hence  the 
load  on  strip  A  B  increases  in  the  same  relation.  Fig. 
4,  at  (b),  illustrates  the  loading  on  strip  A  B.  The 
bending  moment  at  the  center  of  span  for  the  uniform 
load  of  intensity  l/2  w,  is  wL2  -f-  16.  For  the  load  in- 
creasing from  zero  at  middle  of  span  to  Vzw  at  the  ends, 
it  can  be  shown  that  the  bending  moment  at  the  middle 
of  span  is  w  L2  -~  96.  The  total  moment  at  center  of  span 


This  strip  is  the  critical  strip  of  the  slab.  Reinforce- 
ment can  be  diminished  towards  the  beams  surrounding 
the  slab.  This  diminution  is  not  uniform,  however,  but 
as  the  ordinates  of  a  parabola.  At  a  point  V±L  from  the 
beam  the  reinforcement  must  be  not  less  than  %  of  that 
at  the  center.  A  good  rule  is  to  use  the  same  reinforce- 
ment for  the  middle  half  of  the  span  and  uniform  varia- 
tion from  the  quarter  points  to  a  minimum  at  supports. 

For  the  beams  supporting  this  slab  an  intensity  of  load 
may  be  assumed  equal  to  the  reaction  of  strip  A  B,  or  1-3 
w  L.  Assuming  a  uniform  load  on  the  beams  we  find 

Moment  = 


If  the  beam  supports  two  equal  square  slabs,  moment  = 

2^1(9) 
12 

It  is  to  be  noted  that  this  is  the  same  moment  as 
would  be  obtained  by  assuming  that  each  beam  on  the 
side  of  the  square  supports  a  load  uniformly  increasing 
from  ends  to  middle  of  span,  being  Vz  wL  at  middle  for 
each  square  of  slab  supported.  In  using  this  formula  w 
should  be  taken  as  the  weight  per  sq.  ft  of  slab  plus  the 

287 


uniform  live  load  per  sq.  ft.  The  weight  of  the  beam 
itself  below  the  slab  is  a  uniform  load  whose  moment  is 
found  in  the  ordinary  way. 

Exactness  is  not  claimed  for  this  theory.  It  is  based 
on  reasonable  assumptions,  however. 

On  account  of  the  fact  that  the  cross  rods  in  the  slab 
cannot  occupy  the  same  position  the  reinforcement  must 
be  proportioned  accordingly. 

In  a  rectangular  slab  supported  on  four  sides  and  ob- 
long in  shape  the  amount  of  reinforcement  needed  in  the 
two  directions  is  found  as  shown  in  Fig.  50.  It  will  be 
seen  by  trial  that  when  there  is  much  difference  between 
the  sides  of  the  oblong  the  short  span  will  take  nearly  all 
of  the  load.  Thus  when  one  side  is  50  per  cent  longer  than 
the  other  k  =  I,  showing  that  in  an  oblong  slab  of  these 
proportions  reinforcement  in  the  long  direction  needs  to 
be  only  nominal. 

As  an  illustration  of  the  application  of  the  above  to  a 
floor  in  square  slabs,  take  the  case  of  columns  spaced  15 
feet  each  way,  live  load  100  Ib.  per  sq.  ft.  Assuming  a 
weight  of  slab  of  70  Ib.  per  sq.  ft.  we  have  by  equation 
(7)  a  total  moment  on  one  foot  width  of  slab  =  2,790 
ft.-llx  By  equation  (4)  we  find  a  depth  of  slab  of  about 
5%  in.  One  and  one-quarter  per  cent  of  3  in.  x  5^  in. 
would  require  just  a  little  more  than  7-16  in.  square  rods. 
This  size  of  rod  could  be  used,  spaced  3  in.  apart  and  % 
in.  above  the  bottom  of  slab,  but  this  would  not  leave  room 
below  for  the  layer  of  rods  in  the  other  direction,  with 
sufficient  concrete.  To  meet  the  difficulty  we  will  add  ^4 
in.  to  the  depth  of  slab  and  make  the  plane  separating 
the  two  layers  of  rods  one  inch  from  the  bottom  of  slab. 
The  spacing  of  3  in.  will  be  used  for  the  middle  seven 
feet,  increasing  to  12  in.  towards  supporting  beams.  To 
take  care  of  the  continuity  every  alternate  rod  in  the  mid- 
dle half  of  slab  will  be  brought  up  near  the  top  of  slab  at 
quarter  points,  all  other  rods  being  straight.  This  will 
make  a  sort  of  square  basin  in  the  middle  of  the  slab. 

Assume  a  beam  supporting  the  slabs  of  a  depth  of  24 
288 


1- 


•s.. 


JL 

^D 


K__£___ 


* 


I* 


f 


<® 


•y-j 

5 


Equation  ofe/a£>fic  //ne  (Orig/n  c?f  o) 

-*z  «' 


96 

O&f/ecfion    of   o  - 


•Z&&OE1I 


for  equa/  def/ecf/ons 


334  El  2880  El          .  2>84EI     288OE/ 

living     H  _   75L/+-/4L?4 


Moment  on  sfian 


289 


in.,  including  slab,  and  a  weight  of  200  Ib.  per  ft.  below 
the  slab.  By  equation  (9)  the  total  moment  from  the  slab 
is  47,800  ft.-lb.  Adding  5,630  ft.-lb.,  due  to  weight  of 
beam,  we  have  a  total  of  53,430  ft.-lb.  By  equation  (6) 
we  find  the  width  of  beam  to  be  iol/2  in.  The  reinforce- 
ment can  be  made  up  of  four  %-in.  square  rods,  two  of 
which  curve  up,  as  in  Fig.  i,  and  pass  into  adjacent  spans. 
At  the  middle  of  span  all  rods  are  2^6  in.  from  bottom 
of  beam. 

Comparing  this  floor  with  the  one  worked  out  above  hav- 
ing slab,  beams,  and  girders,  we  find  that  the  one  having 
beams  and  girders  contains  about  124  cu.  ft.  of  concrete 
per  bay  or  square,  while  the  other  contains  about  148  cu. 
ft.  The  forms  would  be  simpler  in  the  square  slab  con- 
struction, and  this  would  tend  to  balance  the  cost. 

A  reinforced  concrete  building  should  be  tied  together 
as  a  unit,  just  as  a  building  having  a  steel  frame  is  tied 
together  by  the  rivets  that  connect  the  beams  to  columns. 
This  can  best  be  effected  by  making  rods  in  beams  and 
slabs  continuous,  either  by  connecting  them  end  to  end 
with  turnbuckles  or  by  lapping  them  over  supports.  It  is 
hard  to  see  how  a  failure  of  any  considerable  extent  could 
take  place  in  a  building  so  tied  together,  even*  under  the 
severest  conditions,  assuming  that  the  columns  are  prop- 
erly designed. 

In  the  execution  of  plans  for  reinforced  concrete  it  is 
very  essential  to  have  steel  placed  just  where  calculations 
show  that  it  should  be  placed.  This  is  not  always  easy 
to  do,  especially  in  any  complicated  design.  Permanent 
templates  left  in  the  concrete  may  work  an  injury  by 
making  a  plane  of  cleavage  for  the  starting  of  a  crack. 
Exactness  in  placing  the  steel  may  be  secured  in  the  fol- 
lowing manner: 

Given  a  beam  having  reinforcing  rods  placed  as  per  Fig. 
6,  at  any  given  section.  A  template  of  wood  is  made  fit- 
ting the  cross  section  of  the  beam  and  extending  up  above 
the  slab  6  or  8  in.  Holes  are  bored  in  this  template  for 
each  of  the  reinforcing  rods.  It  is  then  sawed  through 

290 


these  holes  into  pieces  that  can  be  turned  and  removed 
from  the  box  which  forms  the  mold  for  the  beam.  It 
could,  of  course,  be  made  of  several  pieces  fitted  together. 
When  in  use  the  parts  are  clamped  together  as  in  the  fig- 
ure, with  the  rods  passing  through  the  holes.  Enough  of 
these  templates  should  be  used  to  hold  the  rods  in  position 
during  placing  of  the  concrete.  When  the  concrete  has 
been  placed  nearly  to  the  template  on  both  sides,  the  rods 
will  then  be  held  by  the  concrete  itself.  The  templates 
may  then  be  undamped  and  the  pieces  turned  and  drawn 
out,  and  the  concreting  completed. 


IB:  ! 

iZEMl 

I 

< 

f 

^( 

< 

1 

>, 

~n 

^/^ty/^/^&fts 

9 

g 

^S^^^s^Nj 

l 

s 

W/Y///////. 

2 

FIG.  6. 
DISCUSSION  OF  T  BEAMS  AND  SLABS. 

Editor  Concrete  Engineering: 

The  article  by  Mr.  Edward  Godfrey  in  your  issue  of 
Jan.  I,  was  an  excellent  one,  and  if  the  many  good  recom- 
mendations which  it  contained  were  generally  followed 
the  number  of  failures  in  reinforced  concrete  constructions 
would  no  doubt  be  greatly  reduced,  if  not  wholly  elim- 
inated. Reinforced  concrete  has  lately  received  a  bad  rep- 
utation, and  any  rules  and  recommendations  which  tend 
to  spread  knowledge  on  the  subject,  and  influence  design- 
ers and  superintendents  to  exercise  better  judgment  and 
care  in  the  execution  of  their  work,  are  very  welcome. 

Referring  to   the  clause   in   the   article   dealing   with   T 

beams,   the   writer,   although   admitting   that   it   is   on  the 

side  of  safety,  believes  that  it  is  unnecessary  extravagance 

to  figure  beams,  in  the  .way  -recommended  by  Mr.  God- 

291 


^ 


/s-o- 


32" 


Live  ffoor 
A/ternafive  2  '--  Par 


S  /<?£>:- 


r?  ffe  foam  ca/- 

$. 
-  SfeeA  /0% 


s*  ?  65  off"- 


292 


G/rders  ••- 


6.0 >s#  in. 


ALT.  II.  FLOOR  SLAB  DISREGARDED 
IN  CALCULATING  BEAMS  AND  GIRD- 
ERS. 

RESPECTIVE  BENDING  MOMENTS  AND 
DEPTHS  OF  FLOOR  MEMBERS  REMAIN 
THE  SAME  AS  FOR  ALT.  I. 

SLAB:  REMAINS  THE  SAME  AS  FOR 
ALT.  I. 


§•§ 

«  o 


.1 


J3_* 

"?! 

<»   H 


U          O 

-so       q 

i 


s 


-20' 


ALT.  II  IS  CONSEQUENTLY  13.9 
CENTS  MORE  EXPENSIVE  PER  SQ.  FT. 
OF  FLOOR  THAN  ALT.  I— OR  ABOUT 
50<&. 

THE  COST  OF  CENTERING  WOULD 
ALSO  BE  IN  FAVOR  OF  ALT.  I. 


V  r»  <^ 

*J  f*5  M  <*5 

C  *?  ?  ^ 

o  q  9  q 


:    p    w 

•s  ii 

oo  «  O 


293 


frey.  It  is  safe  to  say  that  in  more  than  50  per  cent  of  all 
the  reinforced  concrete  structures  built  in  this  country, 
and  in  Europe,  the  beams  have  been  treated  as  T  beams, 
i.  e.,  a  portion  of  the  floor  slab  has  been  considered  as 
forming  part  of  the  beam,  in  calculating  the  strength  of 
the  same. 

The  fact  that  nearly  all  of  these  structures  are  standing 
today  and  carry  the  loads  for  which  they  were  designed, 
is  at  least  partial  proof  that  this  method  of  calculation  re- 
sults in  a  sufficiently  safe  design. 

The  question  of  how  much  of  the  slab  may  be  safely 
considered  as  part  of  the  beam  is  a  matter  which  should 
be  determined  by  tests.  The  writer  usually  assumes  that 
about  1-5  of  the  span  on  either  side  of  the  beam  acts  as 
top  flange.  This  assumption  is  based  on  the  condition 
that  the  floor  slab  is  built  monolithic  with  the  beams  and 
girders,  and  that  the  slab  reinforcement  is  carried  across 
the  beams  continuously,  and  tied  down  into  the  beam  re- 
inforcement, by  means  of  stirrups  or  hangers.  Such  a 
slnb  may  be  considered  as  a  practically  built-in-beam,  in 
which  case  the  point  of  contra  flexure  occurs  at  a  dis- 
tance of  (0.21  /)  from  the  beam,  for  uniform  loading. 
(See  illustration.)  Within  this  distance  the  upper  part 
of  the  slab  is  in  tension,  and  the  lower  part  in  compres- 
sion, due  to  negative  bending  moments  in  the  slab.  In 
addition  to  these  stresses  the  bending  of  the  beam  pro- 
duces compressive  stresses  in  the  slab  at  right  angles  to 
the  former.  The  latter  have  their  maximum  intensity  at 
the  top  and  tend  to  increase  the  tensile  stresses,  which  are 
resisted  by  the  slab  reinforcements,  and  are  practically  nil 
at  the  bottom.  It  is  often  found  impracticable  to  raise 
the  slab  reinforcement  over  and  adjacent  to  the  beams, 
so  as  to  fully  resist  the  tensile  stresses,  in  which  case,  it 
is  necessary  to  introduce  small  secondary  rods  of  the  re- 
quired section  and  length  near  the  top  of  the  slab,  as  the 
concreting  proceeds. 

VThat  a  considerable  economy  is  effected  by  considering 
the  beams  of  T  section,  as  compared  with  rectangular  sec- 

294 


tion  in  designing,  is  apparent  from  the  example  given  be- 
low, which,  it  is  believed,  represents  an  average  case.  The 
calculations  of  the  beams  and  slabs  are  based  on  the  reg- 
ulations governing  the  design  of  reinforced  concrete  work 
in  New  York  City. 

Apart  from  the  matter  of  economy,  the  beams  which 
are  figured  as  rectangular  become  very  clumsy,  and  would 
be  objected  to  in  many  buildings  on-that  account  alone. 

A.  JORDAHL. 


Editor   Concrete   Engineering: 

Sir:  The  letter  from  Mr.  A.  Jordahl  in  your  issue 
of  Feb.  15,  in  favor  of  the  T-beam  calculation  of  rein- 
forced concrete,  seems  to  me  to  prove  something  that  is 
manifest  and  to  pass  without  comment  the  issue  brought 
up  by  my  article  in  the  issue  of  Jan.  I.  I  do  not  claim 
that  it  is  cheaper  to  neglect  the  floor  slab  in  calculation 
of  the  beams.  If  the  concrete  is  needed  around  the  rods 
to  grip  them  and  to  take  up  the  effect  of  differential  ex- 
pansion, it  should  be  there  for  that  purpose,  and  means 
should  not  be  sought,  through  some  hokus  pokus  of 
methods  of  calculation,  to  leave  it  out  for  the  sake  of 
cheapness  or  supposed  economy.  I  do  not  mean  by  this 
to  question  the  regularity  of  Mr.  Jordahl's  calculation. 
I  have  not  checked  his  figures,  but  take  them  to  be  right 
according  to  some  method  or  other  of  calculation.  What 
I  wish  to  say  is  that  any  method  of  calculation  that  re- 
quires in  a  girder  having  426  sq.  in.  of  concrete,  6  sq.  in. 
of  steel,  and  in  another  of  the  same  depth,  having  800 
sq.  in.  of  concrete,  9  sq.  in.  of  steel  to  perform  the  same 
work,  is  radically  wrong. 

According  to  this  method  of  calculation  a  beam  of  a 
certain  depth  can  have  nearly  half  of  its  concrete  shaved 
off  and  1-3  of  its  steel  without  affecting  its  strength;  or 
conversely,  if  nearly  100  per  cent  be  added  to  the  con- 
crete of  a  beam,  leaving  the  steel  the  same,  it  will  be 
weakened  one-third  on  account  of  being  shy  that  amount 
in  tensile  strength  of  the  steel.  This  difference  is  of 
295 


course  due  to  the  shifting  of  position  that  the  neutral 
axis  is  supposed  to  undergo.  The  method  used  by  Mr. 
Jordahl  to  locate  the  neutral  axis  is  purely  theoretical, 
and  it  is  theoretical  in  a  dangerous  way,  in  that  it  leaves 
out  of  the  account  the  one  most  important  consideration, 
namely,  the  effect  of  the  shrinking  of  the  concrete  in 
setting.  Furthermore,  tests  do  not  in  any  way  substan- 
tiate the  results  of  this  theory. 

A  fault  in  the  girder  preferred  by  Mr.  Jordahl  is,  that 
he  has  6  sq.  in.  of  steel  in  a  girder  only  10  in.  wide.  If 
this  were  made  up  of  6  i-in.  sq.  rods,  there  would  be  only 
2-3  of  an  inch  between  them.  It  does  not  seem  possible 
for  the  concrete  to  grip  effectually  this  amount  of  steel 
and  to  overcome  the  effect  of  differential  expansion  due 
to  temperature  changes.  I  have  seen  beams  3  in.  wide 
with  i^-in.  sq.  rods  in  them  cracked  up,  under  the  dead 
load  alone,  in  a  way  that  tended  to  prejudice  one  against 
reinforced  concrete  construction.  Under  load  the  beams 
resembled  a  string  of  beads. 

To  reiterate,  my  position  is  this :  If  the  neutral  axis 
be  taken  at  the  center  of  depth  of  the  concrete  beam, 
where  tests  have  shown  it  to  be,  the  only  saving  in  a 
T-beam  over  a  rectangular  beam  is  in  concrete  in  the 
lower  part  of  the  rectangle,  and  the  concrete  is  needed 
here  to  protect  and  grip  the  steel.  The  steel  in  each  case 
would  be  exactly  the  same  in  amount. 

EDWARD  GODFREY. 


FLOOR  SLAB  CONTROVERSY  CONTINUED. 
Editor  Concrete  Engineering: 

Sir:  Permit  me  to  say  a  few  words  in  reply  to  Mr. 
Godfrey's  letter  in  your  last  issue.  My  letter  in  your 
issue  of  February  I5th,  merely  attempted  to  show  that 
under  certain  specified  conditions  it  is  entirely  safe  to  in- 
clude part  of  the  floor  slab  in  calculating  the  strength  of 
beams,  and  that  such  procedure  is  attended  with  consid- 
erable economy.  I  did  not  pretend  that  the  (T)  beams  in 
the  example  submitted  were  as  strong  as  those  of  rec- 


tangular  sections,  but  I  did  claim  that  they  were  amply 
strong  to  do  the  work,  and  that  the  rectangular  beams 
involved  a  considerable  waste  of  materials,  due  to  their 
calculation  being  based  on  the  extravagant  assumption 
that  the  floor  slab  did  not  add  to  their  strength. 

It  would  be  interesting  to  have  Mr.  Godfrey  furnish  data 
of  tests  on  reinforced  concrete  T  beams — which  uphold 
his  contention  that  the  neutral  axis  is  at  the  center  of  the 
depth — for  any  percentage  of  reinforcement. 

The  fault  which  Mr.  Godfrey  sees  in  my  girder,  in  that 
it  had  6  sq.  in.  of  steel  in  a  width  of  10  in.,  is  not  as  serious 
as  he  imagines.  The  6  in.  sq.  bars  would  be  placed  in  2 
horizontal  rows,  the  underside  of  the  first  row  il/2  in.  from 
the  bottom  and  with  a  clearance  of  il/2  in.  between  the 
lower  and  upper  row.  The  bars  in  each  row  would  be 
placed  with  2  in.  clearance  and  il/2  in.  from  the  sides  of 
the  girder.  To  insure  the  steel  being  placed  in  its  correct 
position  in  the  beam  box,  and  held  there  while  the  con- 
creting proceeds,  it  is  necessary  to  make  it  up  into  frames 
or  units,  provided  with  saddles  and  spacers,  and  for  that 
reason  it  is  more  practicable  to  place  the  steel  in  2  hori- 
zontal rows,  even  if  there  are  only  4  rods  in  the  beam. 
This,  of  course,  reduces  the  effective  depth  of  the  beam  a 
little,  but  that  is  more  than  offset  by  the  increased  security 
and  ease  of  handling  and  placing  the  steel. 

In  conclusion,  I  have  seen  a  large  number  of  concrete 
beams  6  to  10  in.  wide,  designed  as  T  beams  and  carrying 
test  loads  often  several  times  that  for  which  it  was  de- 
signed, without  showing  any  cracks  or  other  evidence  of 
weakness. 

A.  JORDAHU. 


Editor  Concrete  Engineering: 

SIR:      Replying   to    Mr.    Jordahl's   letter,    in   rebuttal    I 
would  state  briefly  that  if  he  did  not  pretend  that  the  T 
beams  in  his  comparison  were  as  strong  as  the  rectangular 
297 


beams,  why  did  he  compare  them  in  cost  in  order  to  dis- 
credit the  rectangular  beam? 

I  cannot  give  any  data  of  tests  on  T  beams  that  will 
prove  that  the  neutral  axis  is  at  the  center  of  the  depth. 
Can  Mr.  Jordahl  give  any  to  prove  that  it  is  not?  Mr. 
Jordahl's  theory  is  entirely  upset  in  the  case  of  rectangular 
beams  by  tests  which  show  the  neutral  axis  close  to  the 
center  for  safe  loads.  Why  should  it  be  held  to  be  good  in 
T  beams?  The  modulus  of  elasticity  of  concrete  varies  all 
the  way  from  one  million  to  five  million.  Now  if  such  a 
peripatetic  value  as  this  is  to  have  any  weight  in  designing 
and  calculating  beams,  where  are  we  at?  The  strength  of 
a  beam  would  be  a  function  of  the  designer's  private  opin- 
ion as  to  what  the  modulus  of  elasticity  ought  to  be. 

EDWARD  GODFREY. 


The  Design  of  Reinforced  Concrete 
Arches. 

The  arch  is  about  the  least  promising  form  of  reinforced 
concrete  design  to  standardize  by  reason  of  the  apparently 
refractory  facts  about  an  arch  and  its  loading.  In  any  in- 
vestigation of  the  stresses  or  the  stability  of  an  arch  as- 
sumptions must  be  made,  since  the  same  degree  of  accuracy 
is  not  possible  in  arches  as  that  which  obtains  in  steel 
frames  or  even  in  reinforced  concrete  beams.  The  prem- 
ises and  assumptions  upon  which  the  following  investiga- 
tion is  based  are  these: 

(i)  Concrete  will  be  considered  to  take  only  compres- 
sio"  (and  the  shear  incident  to  the  joint  action  of  concrete 
and  steel  as  a  beam  to  resist  bending).  The  unit  com- 
pression, or  the  extreme  fibre  stress  on  concrete  will  be 
taken  at  500  Ibs.  per  square  inch.  This  would  not  be  a 
safe  value  on  a  plain  concrete  arch,  but  by  virtue  of  the 
steel  reinforcement,  which  ties  the  concrete  together  and 
relieves  it  of  bending  strains,  the  concrete  thus  held  is 
capable  of  withstanding  with  safety  a  compressive  stress 
of  this  intensity. 

298 


(2)  Steel  will  be  considered  to  take  only  tension.    The 
unit  tension  allowed  will  be  taken  at  10,000  Ibs.  per  square 
inch,  because  at  this  stress,  it  is  believed,  few  if  any  cracks 
will  develop  due  to  the  extension  of  the  steel  under  ten- 
sion. 

(3)  Earth    will   be   considered    to   exert   only   vertical 
force.    It  is  of  course  true  that  earth  has  the  ability,  under 
certain  conditions,  to  exert  horizontal  pressure;  but  it  is 
not  good  engineering  to  depend   for   stability  upon  earth 
exerting  an  active  horizontal  pressure,  unless  the  condi- 
tions are  such  that  a  measurable  deflection  or  movement 
horizontally,  is  not  injurious.    The  compressibility  of  earth 
is  well  known.    Buildings  having  their  foundations  in  earth 
will  settle  gradually  and  often  continuously.    If  an  arch  is 
made  to  depend  for  its  stability  upon  earth  against  which 
it  presses  horizontally,  there  will  be  the  same  tendency  of 
the  earth  to  settle  back  in  the  direction  of  the  pressure,  and 
this  with  a  resistance  but  a  fraction  of  that  of  a  horizontal 
surface  of  earth  against  a  vertical  load.    An  assumption  of 
horizontal  pressure  of  the  earth  fill  over  an  arch  gives  a 
curve  of  stability  for  the  arch  that  is  more  advantageous 
and  would  give  a  more  economical  arch,  but  the  nature  of 
the  case  does  not  warrant  this  assumption. 

(4)  An  arch  will  be  considered  stable  and  safe  if  the 
arch  ring  is  capable  of  resisting  the  thrust  and  bending 
moment   due   to   any   possible   applied   loading,   when   the 
curve  or  polygon  of  equilibrium  is  drawn  in  such  position 
as  to  give  a  minimum  bending  moment,  or  minimum  devia- 
tion from  the  central  line  of  the  arch  ring.    In  the  case  of 
stone  or  plain  concrete  arches  it  is  conceded  that  the  arch 
will  be  stable  if  an  equilibrium  polygon  can  be  drawn,  using 
any  possible  applied  loading,  that  will  pass  within  the  mid- 
dle third  of  all  joints.     The  two  propositions  are  equally 
sound. 

(5)  The  arch  proper  will  be  taken  as  the  part  of  the 
structure  included  between  two  vertical  planes  through  the 
inner  faces  of  the  arch  abutments.     The  rise  of  the  arch 
will  be  taken  as  the  middle  ordinate  of  the  central  line  of 


the  arch  ring,  considering  the  curve  to  terminate  where  it 
pierces  the  planes  above  referred  to.  If  an  arch  be  de- 
signed with  a  curve  at  springing  joining  the  intrados  and 
the  inner  face  of  abutment  wall,  as  will  often  be  the  case 
for  appearance  sake,  this  small  curve  should  have  no 
structural  significance.  The  effective  rise  of  the  arch  is 
only  obscured  by  considering  the  curve  as  having  any 
weight  in  determining  the  rise.  The  intrados  of  the  arch, 
the  extrados,  and  the  median  line  between  these  (the  cen- 
tral line  of  the  arch  ring)  will  in  general  be  close  approxi- 
mations to  arcs  of  circles,  each  having  one  radius.  Embel- 
lishments on  the  intrados,  for  grace  of  outline,  should  be 
considered  as  such  and  omitted  from  the  calculations. 

(6)  The  abutments  of  the  arch  will  be  separately  treated 
as  abutments  and  not  as  part  of  the  arch.    Their  office  as 
anchoring  mediums   for  the  reinforcing  rods  of  the  arch 
will  also  be  recognized. 

(7)  It  is   understood  that  all   calculations   refer  to  a 
foot  in  width  of  the  arch  ring  and  that  the  arch  is  one 
having  fill  in  the  spandrel  up  to  the  floor  level.     For  a 
ribbed  arch  a  modification  can  be  made  by  using  factors 
that  will  represent  the  weight  carried  by  one  foot  in  width 
of  the  rib.    The  arch  will  be  taken  as  hinged  at  the  abut- 
ments. 

Fig.  i  gives  a  typical  form  of  arch.  The  intrados,  ex- 
trados, and  median  line  are  here  shown  as  arcs  of  circles. 
As  stated  these  curves  will  approximate  circular  curves; 
the  actual  curve  to  be  used  must  be  determined  by  the 
calculations.  Attention  is  called  to  the  method  of  finding 
the  thickness  of  arch  ring.  If  the  intercepts  marked 
"equal"  in  the  figure  are  so  made,  the  thickness  of  arch 
ring  will  be  proportional  to  the  secant  of  its  inclination  to 
the  horizontal,  as  should  be  the  case  where  the  thrust  of 
arch  is  constant.  A  constant  thrust  necessarily  follows 
where  only  vertical  loads  are  considered. 

In  what  follows  earth  will  be  assumed  to  weigh  100  Ibs. 
per  cu.  ft.  and  concrete  150  Ibs. 

For  a  uniform  live  load  of  W  Ibs.  per  sq.  ft.  the  thick- 

300 


ness  at  the  crown  may  be  found  in  the  following  manner. 
The  loads  to  be  considered  are  (i)  the  arch  ring,  (2)  fill 
from  arch  ring  up  to  level  of  crown,  (3)  fill  from  level  of 
crown  to  floor  level.  (This  may  include  paving,  by  mak- 
ing proper  allowance  for  weight  in  value  of  //),  (4)  live 
load.  If  we  find  the  bending  moment  for  these  several 
loads  at  the  center  of  span  and  divide  the  same  by  R,  the 
result  will  be  the  thrust  at  crown.  The  allowed  average 
stress  on  the  cross  section  of  the  arch  will  be  taken  at  250 
Ibs.  per  sq.  in.,  which  would  be  the  average  with  the  ex- 
treme fibre  stress  500  Ibs.  per  sq.  in.  and  intensity  diminish- 
ing to  zero  at  opposite  edge  of  rectangle.  A  small  devia- 
tion of  the  curve  of  equilibrium  will  throw  the  same  one- 
sixth  of  the  depth  out  of  center,  which  would  give  the 
conditions  just  named. 

The  bending  moment  due  to  the  fill  from  level  of  crown 
of  arch  down  (assuming  the  curve  of  arch  a  parabola  and 
remembering  that  the  area  of  the  fill  to  one  side  of  the 
center  is  1-6  5"  R  and  its  center  of  gravity  is  ^  S  from  the 
center  line  of  the  arch)  is 

1005    Rf  S       35\          S*  R 


Now  taking  the  effect  of  the  arch  ring  as  that  of  a  uni- 
form load  10  per  cent  greater  than  the  depth  of  ring  at 
crown  we  have  for  the  total  moment  at  center  of  span 

100  H  S2  ,  165  D  S2 


__ 

~48~~       ~8~        T~  8 

Dividing  the  right  side  of  this  equation  by  R  we  have 
the  thrust,  which  we  have  assumed  to  equal  250  X  *44  D 
(taking  all  dimensions  in  feet.)  Hence  we  have 


From  this  we  may  derive  the  following  value  for  the 
depth  of  arch  ring: 


This  formula  is  to  be  used  only  for  a  trial  depth.     As 
301 


302 


will  be  shown  later  the  effect  of  the  live  load  covering  a 
portion  of  the  span  is  to  produce  an  extreme  fibre  stress 
on  the  concrete  greater  than  the  unit  stress  from  the 
thrust  of  arch  fully  loaded  with  live  load. 

A  little  study  of  some  of  the  curves  of  equilibrium  will 
be  useful  in  the  investigation  of  the  arch. 

A  circular  arc  is  the  curve  of  equilibrium  for  forces 
normal  to  the  curve  itself  and  of  equal  intensity  for  every 
unit  of  length  of  the  curve.  This  curve  is  useful  in  con- 
nection with  arches  because  of  the  ease  with  which  it  can 
be  constructed,  and  because  the  curve  of  equilibrium  for 
an  ordinary  arch  will  not  differ  much  from  a  circular  arc. 

The  catenary  is  the  curve  that  a  flexible  cord  will  as- 
sume from  its  own  weight.  It  is  the  curve  of  equilibrium 
for  forces  parallel  to  each  other  and  of  equal  intensity 
for  every  unit  of  length  of  the  curve.  The  curve  of  equi- 
librium for  an  arch  ring  of  uniform  thickness,  supporting 
the  ring  alone,  is  a  catenary. 

The  common  parabola  is  the  curve  of  equilibrium  for 
forces  parallel  to  each  other  and  of  equal  intensity  for 
every  unit  along  the  chord  of  the  curve.  The  curve  of 
equilibrium  for  a  uniform  load  over  the  entire  arch,  con- 
sidering this  load  alone,  is  a  parabola.  The  fill  over 
the  arch  between  floor  line  and  a  line  parallel  to  the  same 
through  the  crown  would  demand  a  curve  of  the  same 
shape. 

Another  curve  is  one  that  would  support  a  load  repre- 
sented by  the  distance  from  a  horizontal  line  through 
the  crown  of  the  arch  and  the  arch  ring.  Such  a  curve 
would  be  the  curve  of  equilibrium  for  the  fill  over  the 
arch  below  the  level  of  the  crown.  Assuming  the  arch 
ring  of  an  arch  having  a  rise  R  and  a  span  5"  to  be  a 
parabola  whose  equation  is 


we  have  for  the  conditions  in  a  curve  having  the  same 
rise  and  span,  which  would  be  in  equilibrium  under  the 
fill  over  this  parabolic  arch, 

303 


dy  _ihrust  at  {x,  y) 
llx     shear  at  (x,  y) 

The  thrust  at  any  point  is  the  same,  and,  as  we  have 
seen  above,  amounts  to  S2  for  a  load  of  unity  per 
unit  of  area  of  fill.  48 

The  shear  at  (x,  y)  is  1-3  x'  y.  (Note  that  x'  is  the 
absissa  of  the  parabola  and  x  of  the  curve  under  dis- 
cussion, y  corresponding  for  both). 


But  *= 

O 

--^!  X  3  52  =    S* 
dx     48 

Integrating  we  have  jy4=_  ~ 
16/t 

This  is  a  parabola  of  the  fourth  degree. 

The  catenary,  the  common  parabola,  and  the  curve 
whose  equation  has  just  been  deduced  will  each  have  its 
influence  in  determining  the  shape  of  the  curve  of  equili- 
brium, and  hence  the  line  of  the  arch  ring  itself,  in  an 
arch  having  fill  over  the  haunches  and  supporting  a  uni- 
form live  load.  The  curve  will  be  a  sort  of  composite 
of  all. 

Using  the  circular  arc  and  the  parabola  as  standards  by 
which  to  compare  the  other  two  we  find  that  if  all  four 
curves  pass  through  the  same  points  at  ends  and  crown, 
the  catenary  will  lie  between  the  circular  arc  and  the  par- 
abola. For  ordinary  ratios  of  span  and  length  it  will 
be  almost  midway  between  these  curves,  being  a  little 
nearer  to  the  parabola  than  to  the  circular  arc.  The  cir- 
cular arc  will  of  course  be  outside  of  the  parabola.  The 
parabola  of  the  fourth  degree  referred  to  will  be  outside 
of  the  circular  arc.  It  will  be  flatter  at  the  crown  than 
any  of  the  others  and  will  rise  above  the  circular  arc  over 
the  haunches  of  arch. 

The  effect  of  the  fill  in  the  spandrel  of  the  arch  is  to 

make  the  curve  of  equilibrium  to  rise  above  the  circular 

arc  at  the  haunches,  and  that  of  the  weight  of  the  arch 

ring  and  of  the  fill  from  level  of  crown  to  floor  line,  as 

304 


well  as  the  uniform  live  load,  is  to  make  the  curve  drop 
below  the  circular  arc.  The  combined  effect  is  to  make 
the  curve  approach  a  circular  arc,  depending  for  its  loca- 
tion upon  the  predominence  of  these  two  influences. 

In  treatment  of  arches  the  graphic  method  is  generally 
used.  This  method  used  alone  is  crude  and  inexact.  Much 
of  its  inaccuracy  can  be  overcome  by  combining  with  it  the 
analytic  method  to  determine  reactions,  thrusts,  etc.  Thus 
the  horizontal  thrust  of  an  arch  of  a  given  rise  can  be 
found  by  taking  moments  as  for  a  simple  beam  at  the  cen- 
ter of  span:  dividing  the  moment  obtained  by  the  rise 
will  give  the  thrust.  This  thrust  laid  out  to  scale  opposite 
the  middle  point  of  a  vertical  representing  the  consecutive 
applied  vertical  loads  will  give  the  exact  location  of  the 
pole  to  make  the  equilibrium  polygon  pass  through  the 
central  line  of  the  arch  at  crown  and  springing.  This 
avoids  the  usual  cut  and  try  method  employed.  The  sim- 
ple beam  moment  at  any  other  section  is  equal  to  the  prod- 
uct of  the  thrust  and  the  ordinate  of  the  equilibrium  poly- 
gon. Hence  dividing  this  moment  by  the  thrust,  already 
found,  will  give  the  ordinate  of  the  polygon  at  the  section 
under  consideration,  or  the  ordinate  for  the  central  line 
of  the  arch. 

Having  the  approximate  dimensions  of  the  arch  the  cal- 
culations for  the  simple  beam  moment  are  readily  made. 
Of  course  the  arch  could  be  drawn  to  scale,  using  say  a 
circular  arc  for  the  curve,  and  divided  into  vertical  strips 
of  any  desired  width,  and  the  areas  of  these  strips  could 
be  used  to  determine  the  applied  loads.  Then  treating  the 
arch  as  a  simple  beam  or  girder  span  the  bending  moment 
may  be  found  at  center  of  span,  which  divided  by  the 
rise  will  give  the  thrust.  Then  the  simple  beam  moment 
at  any  other  section  may  likewise  be  computed;  dividing 
this  by  the  thrust  will  give  the  proper  ordinate  for  the 
arch. 

It  is  believed  the  following  method  will  give  results,  in 
any  ordinary  case,  that  are  commensurate  in  accuracy  with 
the  common  assumption  of  the  weights  of  concrete  and 
305 


earth.  The  uniform  live  load,  the  fill  above  crown,  and 
the  total  weight  of  arch  ring  can  be  taken  as  a  uniform 
load  over  the  arch.  To  find  the  bending  moment  at  any 
section  assume  one-half  of  this  total  weight  as  concen- 
trated at  that  section,  treating  the  arch  as  a  simple  beam. 
The  moment  due  to  weight  of  fill  below  crown  level  is 


where  y  =  distance  from  center  of  span  to  section  consid- 
ered. This  is  the  moment  for  a  parabolic  curve  for  top 
of  arch  ring. 

Having  found  several  points  in  the  arch  ring  the  curve 
can  be  drawn  through  these  points. 

The  effect  of  live  load  on  part  of  the  span  in  altering 
the  shape  of  the  equilibrium  curve  is  another  important 
point  to  consider.  This  can  be  best  seen  experimentally 
by  taking  a  cord  already  loaded,  or  a  heavy  cable,  and 
suspending  loads  upon  it.  The  added  load  will  cause  the 
cord  to  dip  in  the  vicinity  of  the  load.  In  general  there 
win  be  a  point  on  each  side  of  the  load,  in  the  new  curve, 
that  will  coincide  with  a  point  in  the  original  curve,  while 
the  part  between  these  points  and  the  end  supports  will 
rise.  By  adjusting  the  length  of  the  cord  one  of  these 
points  could  be  brought  to  any  selected  position.  In  the 
treatment  of  the  arch  the  curve  of  equilibrium  takes  the 
place  of  the  cord  in  the  suspended  system  and  responds  to 
the  shifting  of  the  live  load,  rising  where  the  other  would 
dip,  and  vice  versa.  It  is  plain  that  any  number  of  as- 
sumptions can  be  made  as  to  the  nodes  or  points  in  this 
curve  which  retain  their  original  position.  In  accordance 
with  the  fourth  of  the  premises  given  at  the  beginning  of 
this  article  the  node  will  be  taken  at  such  position  as  to 
make  the  curve  of  equilibrium  to  dip  at  one  side  of  this 
node  by  the  same  amount  a»  it  rises  at  the  other  side, 
measured  vertically. 

By  assuming  that  the  curve  of  equilibrium  for  dead 
and  live  load  is  the  same  as  that  for  the  dead  load  alone, 
and  that  the  two  agree  with  the  center  line  of  arch  ring, 
306 


also  that  the  curve  is  a  parabola,  the  bending  moment  in 
the  arch  can  be  determined  analytically  in  a  manner  to  be 
shown  presently.  It  is  not  meant  that  results  obtained  by 
assumptions  that  appear  to  be  so  loose  as  these  are  to  be 
used  in  the  final  design  of  the  arch.  The  assumptions  af- 
ford a  means  of  determining  the  position  of  live  loads  for 
the  maximum  effect  on  the  arch,  and  supply  a  simple  for- 
mula expressing  this  effect,  the  results  of  which  are  very 
close  to  the  true  results.  The  proper  relation  between  span 
and  rise,  depth  of  arch  ring  and  reinforcement  can  be 
studied  by  this  means  to  an  extent  not  approached  by  any 
graphical  or  other  trial  method. 

If  the  curve  of  equilibrium  for  dead  load  coincides  with 
the  central  line  of  arch  ring,  bending  on  the  arch  ring 
is  eliminated  excepting  for  live  load,  and  we  are  left  free 
to  investigate  the  effect  of  a  concentrated  load  or  uniform 
load  covering  part  of  the  span  with  the  arch  as  a  simple 
curved  line. 

In  Fig.  2  A  O  B  represents  the  curve  of  an  arch  shown 
in  the  position  in  which  a  parabola  is  generally  consid- 
ered to  be  placed  with  respect  to  the  axes  of  co-ordinates. 
For  a  concentrated  load  P,  the  triangle  A  F  B  is  an  equilib- 
rium polygon.  If  the  distances  D  C  and  F  E  are  equal, 
this  polygon  is  the  one  giving  the  minimum  moment  on 
the  arch.  The  amount  of  this  moment  is  v  times  the 
thrust  in  the  polygon.  The  various  relations  shown  in 
Fig.  2  may  be  deduced  from  the  properties  of  a  parabola. 
The  moment  on  the  arch  may  then  be  expressed  in  the 
following  equation: 

-2.4142*') 


For  the  position  of  P,  to  give  the  maximum  value  to 
this  moment,  we  equate  the  first  differential  coefficient  of 
this  expression  to  zero.  The  value  of  z  thus  found  is 
.3305*.  A  concentrated  load  would  then  be  placed  two- 
tenths  of  the  span  length  from  one  end  of  the  span  in 
order  to  give  the  maximum  bending  moment  on  the  arch 
ring. 

307 


Reaction-  -|  (S- 2.4142  Z-.S 


2.4142  Z- 


(a) 


Load  W  per,  ff. 


308 


Substituting  the  above  value  of  z  in  (4)  we  have 


For  two  concentrations,  as  at    (a)   Fig.  3,  the  equation 
for  the  bending  moment  in  the  arch  ring  is 


For  the  maximum  value  of  M2  we  find  by  differentiating 
and  equating  to  zero 

19.312*  —  18.49  S/  +  4S22  =  2  Q  (Ss  —  ^) 

The  value  of  z  is  seen  by  this  to  depend  upon  that  of  Q. 
The  following  have  been  worked  out: 

If  Q  —  i/io  S,  z  —  .3085,  M2  =  .osiPS. 

If  Q  =  2/10  S1,  *  =  .2875,  M2  —  .040PS. 

HQ  =  3/io  5>  =  .267^,  M2  —  .osiPS. 

If  Q  =  4/10  5>  =  .2485,  M2  =  .025PS.  (7) 

If  Q  be  made  zero,  we  find  that  z  =  .33o5",  which  agrees 
with  the  value  for  a  single  load  as  previously  found.  If  Q 
be  made  =  S  —  2.4142  z,  the  largest  value  of  Q  that  would 
bring  both  loads  on  the  span,  we  find  that  z  —  .248  S. 
Hence  a  greater  value  of  Q  need  not  be  considered  than 
this,  which  is  four-tenths  of  S. 

For  uniform  load,  as  at  (&),  Fig.  3,  the  equation  for  the 
bending  moment  in  the  arch  ring  is 

Differentiating  this  and  equating  to  zero  we  obtain  for 
the  position  to  give  the  maximum  moment  on  the  arch 
z  —  .248  S.  Substituting  in  (8)  we  have 


This  agrees  with  the  last  equation  of  (7),  if  P  be  made 
.4W,  as  it  should. 

We  thus  see  that  the  maximum  effect  of  any  live  load 
in  producing  bending  is  obtained  when  the  load  covers 
four-tenths  of  the  arch. 

The  foregoing  considers  only  the  bending  moment  on 
the  arch  produced  by  the  live  load,  and  not  the  varying 
thrust  due  to  the  shifting  position  of  the  load.  It  is  there- 
309 


fore  applicable  to  the  steel  reinforcement  only,  as  the 
steel  is  assumed  to  be  stressed  only  by  bending  on  the 
arch  ring  and  not  by  direct  load  or  thrust.  For  the  posi- 
tion of  live  load  to  give  the  maximum  effect  on  the  con- 
crete we  should  derive  an  expression  that  will  combine  the 
extreme  fiber  stress  due  to  bending  and  the  unit  load  due 
to  the  thrust  or  direct  compression.  Taking  the  differ- 
ential coefficient  of  such  expression  and  equating  it  to 
zero  we  would  find  the  position  of  live  load  that  will  give 
the  maximum  effect  on  the  concrete.  The  writer  worked 
out  the  problem  along  these  lines  and  found  that  the  re- 
sulting equations  involved  R  and  D  as  well  as  5"  and  Q. 
However,  by  assuming  ratios  between  R  and  D  both  these 
terms  could  be  eliminated.  Using  wide  variations  in  the 
ratios  of  R  to  D  it  was  found  that  the  values  of  z  that 
satisfied  the  equations  were  practically  equal  to  those  found 
by  considering  the  bending  moment  alone.  This  is  be- 
cause of  the  relatively  greater  effect  of  the  bending  mo- 
ment as  compared  with  the  thrust  in  producing  stress.  The 
equations  expressing  the  maximum  bending  moments  on 
the  arch,  as  already  given,  will  then  be  used  both  in  dis- 
cussing the  proportions  of  the  arch  ring  and  the  reinforcing 
steel. 

This  treatment  of  the  reinforced  concrete  arch  demands 
practically  constant  reinforcement  near  both  top  and  bot- 
tom surfaces  of  the  arch  ring  from  end  to  end,  with  rods 
running  into  the  abutment  for  anchorage.  The  reason  for 
this  uniform  reinforcement  is  seen  by  an  inspection  of 
Fig.  4.  In  this  figure  the  center  line  of  arch  is  represented 
by  the  line  A  O  B.  The  bending  moment  due  to  a  single 
load  rolling  across  the  span  is  represented  by  the  vertical 
distances  from  A  O  B  to  the  curves  A  M  N  and  Q  R  B. 
The  bending  moment  due  to  uniform  load  advancing  across 
the  span  is  represented  by  the  vertical  distances  from 
A  O  B  to  curves  A  T  U  and  Q  V  B.  It  is  here  seen  that 
the  bending  moment  is  pretty  generally  distributed  in  the 
length  of  the  arch,  so  that  no  part  of  the  arch  can  be 
lacking  in  reinforcement.  The  bending  moment  is  of  op- 
310 


posite  sign  for  load  coming  on  from  the  right  and  from  the 
left,  showing  the  need  of  reinforcement  near  the  top  and 
bottom  of  arch  ring  from  end  to  end  of  span. 

Taking  up  first  the  steel  reinforcement  we  will  assume 
that  1 54  per  cent  of  steel  area  is  to  be  used,  ^  of  i  per 
cent  near  the  upper  surface  and  the  same  amount  near  the 
bottom  surface  of  the  arch  placed  %  D  from  the  surface. 
Referring  to  the  writer's  article  on  beams  and  slabs,  pub- 
lished in  Concrete  Engineering,  Jan.  15  and  Feb.  i,  1907, 
it  will  be  seen  by  equation  (i)  that  for  a  reinforcement 
of  i  }4  per  cent  at  the  bottom  of  a  slab  the  allowed  bending 
moment  for  rolling  loads  is  88  <f  per  ft.  width  of  slab,  d 
being  in  inches.  For  $i  of  i  per  cent,  as  here  assumed,  the 
bending  moment,  to  give  the  same  stress  on  the  steel,  is 
44  d2.  Equating  this  to  the  value  of  the  maximum  moment 
from  uniform  live  load,  as  given  in  equation  (9),  and  re- 
ducing the  depth  to  feet,  we  have 

^52=6336JPa        (10) 

In  the  design  of  arches  the  following  live  loads  will  be 
taken  as  standard: 

loo  Ib.  per  sq.  ft.  for  foot  traffic  and  light  vehicles. 

200  Ib.  per  sq.  ft.  for  heavy  driving. 

500  Ib.  per  sq.  ft.  for  trolley  traffic. 

l,ooo  Ib.  per  sq.  ft.  for  steam  roads. 

The  latter  is  the  live  load  found  by  taking  an  axle  load 
of  60,000  Ib.  uniformly  distributed  over  a  space  5  by  12  ft. 
The  load  of  500  Ib.  per  sq.  ft.  is  probably  greater  than  any 
live  load  at  present  specified  for  trolley  traffic,  but  the 
experience  of  steam  railroads  teaches  that  it  is  wise  to 
anticipate  heavier  loading.  It  is  especially  so  in  a  struc- 
ture of  the  permanence  of  a  reinforced  concrete  arch  and 
one  which  has  so  little  possibility  of  being  reinforced  sub- 
sequent to  its  construction  or  used  again  for  another  loca- 
tion having  lighter  traffic. 

Reverting  to  equation  (10),  if  we  let  W  =  loo,  200,  500, 
1,000,  we  find 

S  =  So  D  for  light  traffic. 

311 


S  rr  56  D  for  heavy  traffic. 

S  —  36D  for  trolley  traffic. 

S  —  2^D  for  steam  roads,     (n) 

These  ratios  of  span  to  depth,  while  not  intended  for 
final  use  in  design,  are  of  use  in  fixing  upon  a  close  ap- 
proximation of  the  final  proportions.  The  economical  pro- 
portions can  readily  be  studied  by  means  of  equation  (10). 
If  more  steel  be  used  than  i%  per  cent,  a  less  depth  can 
be  employed  than  that  given  by  equations  (n),  and  if 
less  steel,  a  greater  depth  is  needed.  Steel  reinforcement 
is  affected  only  by  the  live  load,  and,  as  seen,  is  inde- 
pendent of  the  rise  of  the  arch,  except  as  the  rise  is  gov- 
erned by  the  depth  assumed. 

To  take  into  account  the  effect  of  live  load  on  the  con- 
crete we  will  consider  the  arch  as  being  loaded  for  4-10  of 
the  span,  giving  the  moment  as  shown  in  equation  (9).  By 
the  principles  of  mechanics,  in  a  rectangle  having  a  width 
B  and  depth  D 


66  D 

where  M  is  the  bending  moment,  K  is  the  extreme  fiber 
stress,  and  A  is  the  area  of  the  rectangle.  But  K  A  being 
the  product  of  fiber  stress  and  area  may  be  called  an 
equivalent  direct  stress,  for  if  we  divide  this  by  the  area 
we  obtain  the  fiber  stress.  Applying  this  in  equation  (9). 
we  have  for  an  equivalent  direct  load  L  on  the  arch 

<»> 


Under  the  same  loading,  from  the  expression  for  thrust 
as  given  at  (fc),  Fig.  (3),  we  find  it  to  be 

(13) 


We  can  now  modify  the  derivation  of  equation  (i) 
to  include  the  effect  of  live  load  on  a  portion  of  the  span 
only.  The  allowed  thrust,  instead  of  being  taken  at  36,000 
D  to  allow  for  a  possible  bending  moment  due  to  irregu- 
larities, will  be  taken  as  72,000  D,  as  we  now  have  a  definite 
bending  moment,  which  is  a  large  factor  in  producing  an 
312 


equivalent  direct  stress  as  a  component  part  of  that  thrust. 
The  second  term  on  the  right  hand  side  of  the  equation 
just  above  (i)  will  now  be  the  value  in  equation  (13),  and 
a  new  term  will  be  added,  namely,  the  value  of  L  in 
equation  (12). 

Hence  we  have,  as  an  equation  expressing  the  propor- 
tions necessary  in  an  arch  whose  central  line  coincides  with 
the  curve  of  equilibrium  for  dead  load,  the  maximum  effect 
of  live  load  being  considered,  the  following: 


Both  equations  (i)  and  (14)  should  be  made  use  of  in 
finding  the  depth  of  an  arch,  and  the  depth  that  is  the 
greater  should  be  employed.  For  concentrated  loads  equa- 
tion (14)  may  be  modified  by  altering  the  second  and  last 
terms  on  the  right  hand  side  in  accordance  with  the  par- 
ticular loading  used. 

If  for  trial  we  make  H  —  D,  using  the  ratios  in  equa- 
tions (n),  and  solve  equations  (i)  and  (14),  we  find  the 
values  shown  in  Table  A.  The  values  in  columns  2,  4,  6 
and  8  are  found  by  equation  (i),  and  those  in  columns  3, 
5,  7  and  9  are  found  by  equation  (14).  The  approximate 
agreement  between  these  rises  for  each  class  of  loading 
suggests  that  the  percentage  of  steel  reinforcement  used, 
namely,  i%  per  cent  of  total  area,  is  probably  close  to  the 
economic  and  proper  amount.  As  this  is  not  far  from  the 
amount  of  steel  used  in  many  arches  already  built,  there 
is  a  further  suggestion  in  the  table,  namely,  that  the  rises 
shown  for  the  various  classes  of  loading  and  different 
spans  will  probably  give  close  to  the  right  proportions. 

It  is  recommended  that  reinforcement  of  an  arch  be 
made  with  round  rods  running  from  end  to  end  of  span 
and  for  a  distance  of  50  diameters  of  rod  into  each  abut- 
ment. They  should  be  spliced,  where  they  join,  with  turn- 
buckles.  Rods  should  lie  */&  of  the  depth  from  both  top  and 
bottom  surface  of  arch.  Sharp  curves  should  be  avoided, 
especially  in  rods  near  the  surface,  for  stress  in  the  steel 
may  cause  the  rod  to  tear  out  a  portion  of  the  concrete. 

313 


in 

W 


w 

ca  u 

<  £ 
HO 


yJjS  I  oo»t^«ot^o?p 


»-i  ^  00  CO  CS  0  CO 
f*  i—  i  CO  *1* 


>  «  oi  w 


§£ 

"S^Q 


!*"| 

*S.9 


c* 
to 


G 

w 
(J 


W  ~ 

P^  J° 

t  H  o 

10  £ 

s  s 


o-Q 
' 


.Swf 

X) 

^  d*^^ 

S  >,— 


CO  00  t~<OOOCO 


.2W  ^ 
J«5> 

X) 


ooMoooeoct 


CU 
(/5 


314 


If  rods  are  placed  2  diameters  from  the  surface,  the  radius 
of  curvature  should  not  be  less  than  about  80  diameters 
of  rod.  If  rods  are  three  diameters  from  surface,  the 
radius  of  curvature  should  be  not  less  than  about  50  diam- 
eters of  rod.  This  is  to  keep  the  shearing  unit  on  the  con- 
crete covering  the  rod  within  safe  limits. 

There  should  be  rods  through  the  arch  laid  across  the 
main  rods  and  wired  to  the  same,  to  tie  the  concrete  to- 
gether in  that  direction  and  to  distribute  the  load  in  a 
transverse  direction.  These  may  have  1-3  to  1-5  the  area 
of  the  main  reinforcing  rods. 

In  the  abutment  it  is  necessary  to  consider  (i)  the  load 
per  sq.  ft.  on  the  soil,  (2)  the  stability  against  overturn- 
ing* (3)  the  stability  against  sliding. 

In  Fig.  I  the  principal  forces  acting  on  the  abutment  are 
indicated  in  the  parallelogram  A  B  C  D.  In  this  parallelo- 
gram D  C  represents  the  force  supplied  by  the  arch  itself. 
This  is  the  resultant  of  the  total  weight  of  arch,  including 
the  live  4oad  supported,  and  the  horizontal  thrust  under  full 
load.  -  The  force  B  C  is  the  weight  of  concrete  and  earth 
lying  directly  above  the  base  E  F  applied  in  the  line  of 
the  resultant  of  these  combined  weights.  A  C  is  the  re- 
sultant of  these  two.  This  latter  line  must  pass  within 
the  middle  third  of  the  base  E  F,  so  as  to  insure  a  con- 
dition of  zero  tension  at  F.  The  maximum  pressure  on 
the  base  will  then  not  exceed  twice  the  average  pressure 
from  the  total  weight  above  given,  considering  this  weight 
as  distributed  on  the  base  E  F.  To  this,  however,  is  to  be 
added  a  load  per  sq.  ft.  equal  to  the  live  load  per  sq.  ft. 
to  allow  for  live  load  over  the  abutment. 

To  provide  against  sliding,  the  direction  of  A  C  should 
be  such  that  its  horizontal  projection  is  not  more  than 
one-half  of  its  vertical  projection.  This  means  that  a  co- 
efficient of  sliding  friction  of  one-half  is  assumed. 

The  dimensions  of  the  abutment  are  to  be  adjusted 
until  the  above  conditions  are  satisfied.  If  the  resultant 
pressure  does  not  fall  within  the  middle  third  of  the  base, 
the  base  must  be  extended  away  from  the  arch.  Also  if 

315 


the  vertical  pressure  on  the  soil  is  too  great,  the  same 
extension  should  be  made;  or  an  offset  may  be  made  on 
the  inner  edge  of  abutment,  if  this  does  not  cause  the  line 
of  pressure  to  fall  without  the  middle  third  of  the  new 
base.  If  the  inclination  of  the  resultant  A  C  is  not  steep 
enough  to  have  a  tangent  of  two,  the  abutment  should  be 
made  deeper. 

The  above  does  not  apply  to  a  rock  foundation.  Where 
the  abutment  rests  on  rock  and  can  be  built  so  as  to  have 
a  bearing  against  a  vertical  rock  surface  to  take  the  hori- 
zontal thrust,  it  need  not  have  mass  enough  to  resist  over- 
turning, for  the  rock  surface  can  be  relied  upon  to  resist 
horizontal  forces.  The  inclination  of  the  resultant  pres- 
sure may,  of  course,  be  less,  as  sliding  is  also  prevented 
by  the  rock. 

As  a  corollary  to  the  foregoing  it  may  be  added  that  the 
same  general  principles  apply  to  stone  arches  or  plain 
concrete  arches,  except  as  they  bear  on  the  steel  rein- 
forcement. In  such  an  arch,  where  the  material  will  not 
take  tension,  the  resultant  pressure  must  not  fall  outside 
of  the  middle  third  of  the  arch  ring. 

Fig.  5  shows  the  conditions  that  will  hold  when  the 
resultant  falls  at  the  edge  of  the  middle  third  of  the  arch 
ring.  Taking  equation  (14)  we  find  that  the  first,  third 
and  fourth  terms  of  the  right  hand  side  of  that  equation 
equal  the  dead  load  thrust,  and  the  second  term  is  the  live 
load  thrust  when  the  live  load  covers  4-10  of  the  span 
from  either  end.  The  distance  %  R  in  Fig.  5  is  the  maxi- 
mum deviation  from  the  arch  ring,  or  v  of  Fig.  2,  under 
the  same  loading.  Making  this  substitution  in  the  equa- 
tion in  Fig.  5  and  reducing  we  have  (if  D  =  H) 


r>_5.  521  £>2+.  0067  WD         /1_, 

.01  ^-.3472  D 
This   expresses   the   relation   between   the    rise   and    the 
depth  of  an  arch  needing  no  steel  reinforcement.     In  such 
an  arch  we  could  allow  an  extreme  fiber  stress  of  400  Ib. 
per  sq.  in.,  or  an  average  at  the  crown  of  200  Ib.  under 
316 


CM 

X 

H 


1 

3     ^ 

£d 

1 

! 

1  E 

3 

1 

o 
J 

i 

8 

£ 

o 

|*k4  Q|vO 

l*-orN- 

J 

317 


full  load.     Following  the   derivation  of  equation    (i)    we 
ly  then  write 

<"> 


By  trial  it  was  found  that  using  the  ratios  of  S  to  D 
given  in  Table  B  the  approximate  agreement  in  values  of  R 
were  found  to  exist  It  is  interesting  to  note  also  that 
these  values  of  R  do  not  differ  greatly  from  those  in 
Table  A. 

It  is  to  be  observed  that  the  arch  of  Table  A  is  propor- 
tioned ort  the  assumption  that  the  steel  reinforcement  is 
stressed  by  any  eccentric  load  on  the  arch  ring.  In  thick 
arches  especially  reinforcement  could  rationally  be  dimin- 
ished by  reducing  the  bending  moment  by  the  amount  that 
the  plain  concrete  would  take.  That  is,  in  refining  the 
calculations  the  distance  v  of  Fig.  2  can  be  diminished  by 
1-6  of  the  depth  of  arch  ring. 

For  short  spans  of  say  20  to  30  ft.,  arches  do  not  seem 
to  be  appropriate.  Flat  slabs  or  straight  beams  and  slabs 
would  seem  to  be  more  suitable.  Horizontal  thrust  is  then 
eliminated,  and  the  abutments  may  be  much  lighter. 


SHORT  ARCH  SPANS. 
Editor  Concrete  Engineering: 

Sir:  In  your  issue  of  March  I,  Mr.  Godfrey  concludes 
an  article  on  "The  Design  of  Reinforced  Concrete  Arches," 
with  the  following  statement:  "For  short  spans  of  say  20 
to  30  ft.,  arches  do  not  seem  to  be  appropriate.  Flat  slabs 
or  straight  beams  and  slabs  would  seem  to  be  more  suit- 
able. Horizontal  thrust  is  then  eliminated  and  the  abut- 
ments may  be  much  lighter." 

I  am  unable  to  discover  any  basis  for  such  a  conclusion. 
The  relations  between  arches  and  beams  of  short  spans 
are  the  same  as  for  arches  and  beams  of  longer  spans.  If, 
then,  a  beam  of  30  ft.  is  more  desirable  than  an  arch  of 
that  span,  why  is  not  a  beam  of  150  ft.  span  more  desir- 
able than  an  arch  of  the  same  span.  The  only  reasonable 
difference  between  the  two  is  in  forms  and  erection  and 
318 


this    difference    is    maintained    for    the    longer    spans    as 
well  as  for  the  shorter. 

I  have  frequently  heard  the  statement  by  engineers, 
similar  to  that  given  above  by  Mr.  Godfrey,  that  the  rea- 
son an  arch  is  not  as  efficient  as  a  beam  is  because  it  has 
horizontal  thrust.  But  that  is  the  very  reason  that  makes 
the  arch  more  efficient  than  the  beam.  The  banks  of  a 
stream  have  horizontal  resistance  as  well  as  vertical  resist- 
ance; why  then  throw  away  the  horizontal  reaction  when 
the  arch  offers  so  satisfactory  a  method  of  using  it  to  re- 
duce the  material  in  the  structure?  If  an  arch  and  a 
beam  of  same  span  and  having  the  same  depth  are  both 
reinforced  to  the  same  extent,  the  beam  will  require  heavier 
abutments  than  the  arch  to  support  the  same  loading  in- 
stead of  lighter  abutments,  as  Mr.  Godfrey's  statement 
would  indicate.  Such  an  arch  would  have  the  same  strength 
as  the  beam  without  exerting  any  horizontal  thrust  at  all. 

The  above  statements  will  doubtless  appear  strange  to 
many  railway  bridge  engineers  who  do  not  understand 
the  arch,  yet  those  same  engineers  will  use  knee  braces  in 
their  beam  culverts,  "to  shorten  the  span,"  as  they  say, 
without  realizing  that  a  logical  conclusion  of  this  form 
of  design  would  be  an  arch. 

DANIEL  B.  LUTEN. 
President  National  Bridge  Co. 


Editor  Concrete  Engineering. 

Sir:  I  have  before  me  a  copy  of  a  letter  from  Mr. 
Daniel  B.  Luten  criticising  my  statement  that  for  short 
spans  arches  do  not  seem  to  be  appropriate,  and  beg  to 
thank  you  for  the  opportunity  to  reply. 

Mr.  Luten  says  he  does  not  discover  any  basis  for  such 
?.  conclusion.  The  basis  is  this:  An  arch  of  short  span 
and  economical  proportions,  so  far  as  the  arch  itself  is 
concerned,  that  is,  eliminating  the  abutments,  as  my  table 
would  show,  would  have  a  small  rise,  say  I  ft.  or  so. 
Now  the  purpose  of  using  any  kind  of  a  structure  to  span 
319 


space  is  to  get  an  opening  for  water  or  passage.  With 
so  low  a  rise  the  arch  would  have  to  be  on  the  top  of  high 
abutments  in  order  to  get  the  opening  necessary.  Again 
with  so  low  a  rise  there  would  be  a  heavy  thrust.  High 
abutments  with  a  heavy  thrust  on  top  would  be  anything 
but  economical. 

I  attempted  to  show  in  the  first  part  of  my  paper  that 
it  is  not  good  engineering  to  depend  on  earth  as  exerting 
an  active  horizontal  pressure.  It  is  well  known  that  earth 
settles  away  from  any  pressure  brought  upon  it.  What 
sort  of  conditions  would  result  if  a  short  arch  of  20  ft. 
span  settled  away  at  the  ends  to  the  extent  of  only  an 
inch  at  each  end?  It  is  especially  true  that  earth  fill 
is  quite  unstable.  This  is  what  would  be  encountered  in 
the  large  majority  of  cases  so  near  the  top  of  an  arch. 
Such  would  be  totally  unfit  to  take  any  horizontal  thrust. 

Mr.  Luten  says  that  the  relation  between  arches  and 
beams  of  short  spans  are  the  same  as  for  arches  and  beams 
of  longer  spans.  I  do  not  see  how  he  can  sustain  such  an 
assertion.  I  do  not  think  that  he  would  attempt  to  make 
or  approve  a  beam  of  150  ft.  of  span,  and  I  do  not  believe 
he  would  condemn  a  flat  slab  for  a  span  of  5  ft.  My 
table  shows  a  much  greater  relative  and  actual  rise  in 
arches  of  long  spans.  These  greater  rises  not  only  allow 
the  clearance  and  opening  necessary,  but  they  also  reduce 
the  relative  thrust  and  bring  the  points  of  its  application 
down  near  the  base  of  abutment.  These  are  very  im- 
portant differences  in  the  relation  between  beams  and 
arches  in  long  and  short  spans. 

Answering  the  latter  part  of  his  third  paragraph  I  would 
say  that  the  "arch"  that  exerts  no  horizontal  thrust  at  all 
is  not  an  arch  at  all.  It  is  simply  a  curved  beam.  A  simple 
truss  span  may  be  given  any  camber,  even  to  a  large  frac- 
tion of  the  span,  and  supported  on  rollers  at  one  end.  It 
is  still  a  simple  span  and  in  no  sense  an  arch.  So  a  steel 
beam  may  be  curved  and  given  only  horizontal  supports. 
It  is  only  a  curved  beam.  An  arch  must  have  thrust  to  be 
an  arch. 

320 


There  is  a  popular  notion,  born  of  little  knowledge,  that 
an  arch  is  the  strongest  form  of  construction.  But  an 
arch  without  abutments  to  take  the  thrust  is  not  an  arch 
and  is  not  strong.  Independent  of  the  effect  of  curving 
on  the  metal  a  curved  I  beam  is  not  as  strong,  simply 
supported,  as  a  straight  one. 

EDWARD  GODFREY. 


CRITICISM    OF    MR.    GODFREY'S    ARTICLES    ON 

ARCHES. 
Editor  Concrete  Engineering. 

In  your  issue  of  April  i,  1907,  I  called  attention  to  an 
erroneous  statement  in  Mr.  Godfrey's  article,  that  short 
beams  were  more  efficient  than  short  arches  and  he  replied 
with  the  remarkable  argument  that  an  arch  proportioned 
for  efficiency  without  considering  the  abutments,  would 
require  such  heavy  abutments  that  the  beam  would  be 
more  economical. 

Mr.  Godfrey  continues :  "It  is  a  popular  notion  born  of 
little  knowledge  that  an  arch  is  the  strongest  form  of  con- 
struction." It  is  quite  true  that  this  notion  is  born  of  little 
knowledge,  for  the  most  inexperienced  stone  mason  learns 
it,  but  it  is  surprising  that  Mr.  Godfrey  fails  to  see  it.  I 
have  been  moved  to  investigate  his  series  of  articles  on 
arches  and  I  find  a  most  remarkable  combination  of  unau- 
thorized assumptions,  too  numerous  to  be  mentioned  in  one 
letter.  I  beg,  however,  to  call  your  attention  to  a  few  on 
the  first  page  of  his  article  in  your  Feb.  15  issue.  In 
(4)  he  states :  "In  the  case  of  plain  concrete  arches  it  is 
conceded  that  the  arch  will  be  stable  if  an  equilibrium  pol- 
ygon can  be  drawn,  using  any  possible  applied  loading  that 
will  pass  within  the  middle  third  of  all  joints."  This 
statement  should  be  "*/  the  proper  equilibrium  polygon  for 
each  arrangement  of  loading  can  be  kept  within  the  middle 
third."  Otherwise  it  is  unsound,  and  his  accompanying 
statement  in  which  he  selects  the  equilibrium  polygon  that 
gives  the  minimum  moment,  is  equally  unsound.  For  an 
arch  hinged  at  the  abutments  this  latter  assumption  will 
321 


hold  good  only  when  there  is  a  shortening  of  the  span  on 
striking  centers,  and  every  builder  of  a  concrete  arch 
knows  that  the  arch  settles  and  the  span  increases  when 
the  centers  are  removed.  The  assumption  might  prove 
good  if  there  were  great  expansion  of  the  concrete  in  set- 
ting, but  in  all  other  cases  it  is  not  only  baseless,  but  is 
actually  on  the  side  of  danger.  Many  of  Mr.  Godfrey's 
conclusions  will  require  modification  because  of  this  error. 

In  (6)  and  (7)  he  states  that  "the  office  of  the  abut- 
ments as  anchoring  mediums  for  the  reinforcing  rods  in 
the  arch  will  be  recognized,"  and  in  the  next  paragraph 
adds  that  "the  arch  will  be  taken  as  hinged  at  the  abut- 
ments." 

In  (3)  Mr.  Godfrey  says  that  "it  is  not  good  engineering 
to  depend  for  stability  on  earth  exerting  an  active  hori- 
zontal pressure."  It  occurs  to  me  that  it  is  good  en- 
gineering to  make  the  base  of  a  retaining  wall  sufficiently 
wide  to  resist  the  overturning  action  of  this  pressure. 
Perhaps  Mr.  Godfrey  meant  to  say  that  the  passive  resist- 
ance of  the  earth  should  not  be  relied  upon,  but  if  so  he 
failed  to  conform  to  that  idea  in  his  arch  design,  for  he 
actually  does  neglect  the  active  horizontal  earth  pressure. 
Yet  every  retaining  wall  proves  that  there  is  such  a  pres- 
sure. 'It  not  only  must  be  depended  upon  for  stability, 
but  if  neglected  it  may  cause  the  collapse  of  the  arch. 
Moreover  the  passive  resistance  of  earth  may  be  relied  on 
to  a  limited  extent,  as  Mr.  Godfrey  himself  shows,  for  his 
abutment  design  allows  varying  intensities  of  stress. 

Many  of  his  assumptions  are  made  to  simplify  his  proc- 
ess regardless  of  consequences,  and  he  labors  to  make 
himself  and  others  believe  that  they  are  justifiable. 

Mr.  Godfrey  is  wrong  in  saying  that  a  curved  beam  is 
not  as  strong  as  a  straight  beam.  The  bending  moments 
on  the  two  beams  are  the  same,  and  the  moments  of  resist- 
ance are  in  favor  of  the  curved  beam  as  an  analysis  will 
readily  show.  If  he  will  compare  beams  and  arches  on 
the  basis  of  waterway  area  he  will  still  find  that  the  arch 
is  the  more  efficient. 

322 


He  suggests  that  I  would  not  approve  a  beam  of  150  ft. 
span.  Certainly  not,  but  merely  because  of  the  cost.  And 
this  is  exactly  the  reason  that  I  urged  against  the  short 
span  beams.  A  beam  of  150  ft.  is  quite  feasible  given 
sufficient  depth  and  material,  but  it  is  exceedingly  ineffi- 
cient as  compared  with  an  arch.  For  shorter  spans  the 
difference  is  not  so  marked,  but  it  is  nevertheless  in  favor 
of  the  arch. 

I  have  not  by  any  means  uncovered  all  the  erroneous 
assumptions  in  Mr.  Godfrey's  article,  and  with  your  per- 
mission will  conclude  in  a  subsequent  issue. 

DANIEL  B.  LUTEN. 


MR.  GODFREY'S  REPLY  TO  THE  FOREGOING. 
Editor  Concrete  Engineering. 

I  beg  to  thank  you  for  the  opportunity  to  reply  to  Mr. 
Daniel  Luten's  second  letter  criticising  my  paper  on  arches. 

In  Mr.  Luten's  first  paragraph  he  tries  to  read  into  my 
statements  an  absurdity  that  does  not  exist.  It  is  per- 
fectly rational  to  design  a  beam  entirely  apart  from  the 
supporting  walls  or  columns.  Does  Mr.  Luten  see  any 
absurdity  in  following  this  with  a  statement  that  this  beam 
requires  walls  or  columns  or  other  support?  It  is  per- 
fectly rational  to  design  an  arch  without  any  reference  to 
what  is  going  to  support  it  and  to  offer  the  necessary  hori- 
zontal thrust  to  make  it  act  as  an  arch.  Is  it  absurd  or 
"remarkable"  then  to  say  that  if  economy  in  such  an  arch 
demands  a  low  rise,  the  supporting  abutments  must  be  very 
heavy  because  the  thrust  is  great? 

Now  an  arch  of  small  span  could  be  made  with  a  large 
rise  in  order  to  get  the  necessary  waterway  under  it,  and 
this  large  rise  would  permit  of  a  small  depth  at  crown  be- 
cause the  thrust  would  be  relatively  small.  So  far,  so 
good.  Theoretically  such  an  arch  would  be  economical  be- 
cause of  the  small  thickness,  for  perfectly  balanced  static 
loads.  If  such  an  arch  be  subjected  to  live  load,  because 
of  the  fact  that  it  is  of  shallow  depth  and  that  it  has  a 
sharp  curve,  the  equilibrium  polygon  would  readily  pass 
323 


away  beyond  the  confines  of  the  arch,  and  the  bending  mo- 
ment would  be  great.  An  arch  of  shallow  depth  would 
offer  but  little  resistance  to  bending  'moments,  and  the 
economy  of  the  arch  goes  aglimmering. 

I  have  heard  men  express  the  opinion  that  camber  in 
a  girder  or  truss  span  is  to  prevent  the  span  from  dipping 
from  a  true  horizontal  line  for  fear  that  the  strength  will 
all  be  gone  when  the  deflection  exceeds  the  camber. 
Others  a  little  better  informed  still  think  that  camber  is 
necessary  to  the  strength  of  a  truss  span,  when  in  fact 
it  does  not  affect  the  strength  in  any  manner,  and  is  sim- 
ply to  prevent  a  dip  in  the  track.  These  notions  are  rudi- 
ments of  misinformation  from  the  days  when  structures 
were  designed  by  judgment,  or,  in  other  words,  guess. 
Are  we  to  return  to  those  days  and  take  our  knowledge 
from  "inexperienced  stone  masons,"  or  are  we  to  continue 
to  analyze  structures  on  the  basis  of  principles  of  mechan- 
ics? I  would  like  to  repeat  my  former  assertion  to  give  it 
emphasis.  An  arch  without  abutments  to  take  the  thrust 
is  not  an  arch  and  is  not  strong. 

I  would  not  have  Mr.  Luten  or  anyone  else  imagine  for 
an  instant  that  my  treatment  of  an  arch  has  anything  of 
the  exactness  of  the  common  treatment  of  steel  structures, 
or  that  it  is  theoretically  correct.  The  first  paragraph  of 
my  paper  sets  this  forth  clearly.  Assumptions  are  abso- 
lutely necessary,  and  a  theoretically  correct  treatment  of  an 
ordinary  stone  or  concrete  arch  is  an  impossibility.  To 
say  that  my  assumptions  are  unauthorized  leaves  me  with 
nothing  to  reply.  One  is  naturally  timid  about  announcing 
himself  as  an  authority.  If  the  assumptions  are  declared 
to  be  unsound,  that  is  a  different  matter.  I  shall  reply 
from  that  standpoint. 

Mr.  Luten's  first  attack  upon  my  assumptions  is  rather 
upon  the  English  with  which  one  of  them  is  clothed  than 
upon  the  assumption  itself.  It  is  instructive  to  note  that 
it  is  the  proper  equilibrium  polygon  that  must  be  used, 
that  is,  not  one  belonging  to  some  other  arch  that  may  be 
laid  out  on  the  board,  but  the  polygon  and  loading  belonging 

324 


to  the.  arch  under  consideration.  As  I  read  literature  on 
arches,  the  proper  equilibrium  polygon  is  arrived  at  by  a 
system  of  cut  and*try  until  a  polygon  is  found  that  will 
fill  the  bill.  Of  course  this  method  is  based  on  authorized 
assumptions,  and  demands  a  drawing  board  and  all  of  the 
necessary  accoutrements  to  make  it  a  first  class  guessing 
match.  It  would  not  do  at  all  to  ascertain  beforehand,  by 
calculation,  as  could  readily  be  done,  where  this  proper 
polygon  will  probably  pass. 

I  cannot  see  how  "each  arrangement  of  loading"  is  any 
more  lucid  than  "any  possible  applied  loading."  I  made  no 
attempt  to  go  into  the  matter  of  explaining  the  well  known 
process  of  determining  the  stability  of  an  arch  by  drawing 
a  polygon  that  will  pass  through  certain  points  in  the  arch, 
and  then,  if  this  fails  to  pass  through  the  middle  third  of 
all  joints,  drawing  another,  and  another,  etc.,  until  one  is 
found  that  will  pass  through  the  middle  third  throughout. 
This  is  known  to  engineers,  and  if  any  others  wish  to  fol- 
low that  way,  they  can  consult  works  on  arches,  where 
this  process  is  fully  set  forth  and  recommended.  My 
treatment  of  plain  concrete  arches  is  nothing  more  nor 
less  than  a  systematic  method  of  finding,  analytically,  how 
deep  an  arch  should  be  in  order  to  assure  the  equilibrium 
polygon  falling  within  the  middle  third. 

I  will  not  discuss  the  soundness  of  this  "authorized  as- 
sumption" until  Mr.  Luten  brings  out  something  more  un- 
derstandable than  the  last  part  of  his  second  paragraph.  I 
might  state,  however,  that  an  arch  that  is  designed  to  give 
a  horizontal  thrust  against  a  vertical  wall  of  yielding  earth 
could  not  be  expected  to  do  anything  else  but  settle  and 
increase  in  span.  This  is  the  very  thing  I  stated  in  my 
previous  letter  as  the  objection  to  an  arch  of  low  rise  and 
small  span.  It  is  objectionable  in  an  arch  of  any  rise  or 
span  to  depend  upon  a  vertical  wall  of  earth  to  take  the 
thrust,  because  the  earth  will  settle  away,  and  the  arch, 
to  an  unknown  extent,  becomes  a  beam. 

In  Mr.  Luten's  third  paragraph  he  tries  to  read  another 
absurdity  into  my  paper.  It  is  because  a  well  designed  arch 
325 


needs  reinforcement  near  the  top  and  bottom  from  end  to 
end  of  span  that  I  would  run  the  reinforcing  rods  into  the 
abutment,  otherwise  there  would  be  no  reinforcement  until 
a  point  was  reached,  some  distance  from  the  abutment, 
where  the  rods  had  sufficient  embedment  in  the  concrete 
to  make  them  effective.  It  is  because  the  abutment  of  an 
arch  would  not  be  suitable  anchorage  for  a  cantilever  that 
it  would  not  be  suitable  to  hold  the  end  of  an  arch  fixed. 
Heavy  abutments  could  be  designed  that  would  be  suitable 
for  taking  the  stress  of  a  fixed  ended  arch,  but  their  econ- 
omy is  very  doubtful. 

Down  in  Palos,  Alabama,  some  years  ago,  I  observed 
some  large  piers  being  constructed  in  earth  that  was 
"candy"  to  dig.  These  piers  not  only  had  vertical  sides, 
but  they  were  chamfered  out  so  as  to  have  a  base  broader 
than  the  section  at  the  ground  level.  All  of  this  excava- 
tion was  done  without  a  stick  of  a  shore  to  keep  the  earth 
from  caving  in.  Where  was  Mr.  Luten's  "active  horizontal 
earth  pressure?"  It  is  not  an  unusual  thing  to  see  trench- 
ing done  in  earth  with  little  or  no  bracing  and  to  see  earth 
standing  in  a  high  vertical  wall  for  some  time.  The  prin- 
cipal forces  against  a  retaining  wall  are  those  due  to  the 
loosening  action  of  rains  or  the  expanding  action  of  frost. 
These  are  wedging  actions.  They  have  no  place  whatever 
on  the  haunches  of  an  arch,  and  they  would  be  broken 
reeds  to  rely  upon  against  the  side  of  an  abutment.  I 
meant  exactly  what  I  said,  and  not  what  Mr.  Luten  thinks 
I  ought  to  have  meant.  The  horizontal  pressure  of  earth 
over  the  top  of  the  arch  may  be  neglected  with  perfect 
safety.  The  horizontal  pressure  of  earth  behind  the  abut- 
ment should  be  neglected  for  safety. 

Mr.  Luten  acknowledges  that  the  bending  moments  of  a 
curved  and  a  straight  beam  are  the  same.  It  would  be  in- 
teresting to  see  the  analysis  that  shows  that  putting  an 
I-beam  through  a  bulldozer  and  curving  it  in  the  plane  of 
the  web,  increases  its  section  modulus.  The  reason  why 
a  curved  beam  is  not  as  strong  as  a  straight  one  is  because 
the  flange  stresses,  which  tend  to  go  in  straight  lines,  will, 


in  a  curved  flange,  induce  secondary  stresses.  These 
stresses  would  tend  to  increase  or  decrease  the  curvature 
of  the  outstanding  flanges,  according  as  the  stress  is  com- 
pression or  tension.  Curved  flanges  of  a  beam  or  girder 
are  just  as  irrational  and  uneconomical  as  bowed  columns 
or  tension  members  (bowed  in  one  direction.) 

Mr.  Luten  says  in  this  letter  that  the  difference  between 
arches  and  beams  is  not  so  marked  in  shorter  spans.  In 
his  former  letter  he  said:  "The  relation  between  arches 
and  beams  of  short  spans  are  the  same  as  for  arches  and 
beams  of  longer  spans."  Mr.  Luten  has  more  confidence  in 
beams  of  reinforced  concrete  than  I  have.  As  an  engineer 
I  would  condemn  a  beam  of  150  ft.  span.  Would  Mr.  Luten 
condemn  a  slab  of  6  ft.  span? 

EDWARD  GODFREY. 


The  Design  of  Foundations. 

The  requisites  of  a  good  foundation  are:  (i)  The  pres- 
sure per  sq.  ft.  on  the  soil  must  not  exceed  a  certain  safe 
limit.  (2)  The  unit  pressure  on  the  entire  foundation 
should  be  as  near  uniform  as  practicable.  (3)  The  pres- 
sure should  never  be  negative,  that  is,  there  should  not  be 
a  tendency  to  lift  the  foundation  which  is  in  excess  of  its 
weight  at  any  part.  (4)  The  foundation  must  be  suffi- 
ciently deep  not  to  have  the  underlying  soil  disturbed.  (5) 
The  materials  must  be  practically  indestructible  in  their 
respective  places.  (6)  The  integrity  of  the  foundation  it- 
self must  be  assured;  that  is,  it  must  be  capable  of  resist- 
ing the  forces  upon  it. 

To  provide  for  the  first  requisite  the  safe  bearing  power 
of  the  soil  must  be  known.  This  is  not  determined  by  ex- 
periment so  much  as  by  experience. 

The  pressures  allowed  by  the  New  York  Building  Code 
per  sq.  ft.  on  various  soils  are  as  follows :  Soft  clay,  one 
ton;  ordinary  clay  and  sand  together,  in  layers,  wet  and 
springy,  two  tons ;  loam,  clay  or  fine  sand,  firm  and  dry. 
three  tons;  very  firm,  coarse  sand,  stiff  gravel  or  hard 
clay,  four  tons.  The  same  building  code  allows  for  tests 
327 


being  made  to  determine  the  bearing  capacity  in  special 
cases.  • 

In  Baker's  Masonry  Construction  the  following  are  given 
as  the  safe  bearing  power  of  soils  in  tons  per  sq.  ft: 
Quicksand,  alluvial  soils,  etc.,  0.5  to  I ;  sand,  clean,  dry. 
2  to  4;  sand,  compact  and  well  cemented,  4  to  6;  gravel 
and  coarse  sand,  well  cemented,  8  to  10;  clay  soft,  I  to  2; 
clay  in  thick  beds,  moderately  dry,  2  to  4;  clay  in  thick 
beds,  always  dry,  4  to  6;  rock,  from  5  up.  This  lower 
value  is  for  rock  equal  to  poor  brick  masonry. 

In  the  case  of  hard  rock  the  area  of  foundation  may 
sometimes  be  determined  by  the  strength  of  the  foundation 
rather  than  that  of  the  rock.  Thus,  if  concrete  is  used  in 
a  pier  with  a  bearing  power  of  15  tons  per  sq.  ft.,  this  sets 
the  limit,  though  the  rock  may  be  capable  of  carrying  a 
greater  load. 

Instability  in  a  foundation,  as  regards  the  bearing  power 
of  the  soil,  is  exhibited  in  the  sinking  or  settling  of  the  su- 
perstructure. This  may  be  the  result  either  of  compressi- 
bility of  the  soil  or  of  lateral  flow  in  it.  The  unit  loads 
above  given  are  those  that  will  generally  give  a  structure 
with  little  or  no  settlement.  On  soils  other  than  rock,  or 
solid  gravel,  or  hardpan  a  little  settlement  is  usually  ex- 
pected and  sometimes  allowed  for  in  fixing  the  level  of  the 
floors. 

Compressible  soils  may  have  their  bearing  power  in- 
creased (i)  by  ramming;  (2)  by  driving  in  short  piles  to 
compact  the  soil  by  this  means;  (3)  by  driving  in  piles 
6  or  8  ft.  and  then  withdrawing  them  and  filling  the  holes 
with  sand,  slag,  gravel,  or  concrete,  well  rammed  in,  or 
the  holes  may  be  made  by  driving  a  cast  iron  cone  20  or  30 
ft.  into  the  soil  and  ramming  the  hole  full  of  the  materials 
named.  The  latter  method  was  employed  in  the  foundation 
of  some  of  the  buildings  of  the  Paris  Exposition,  the  ram- 
ming being  done  with  a  cast  iron  weight  of  I  to  il/2  tons. 
(See  Engineering  News,  Sept.  27,  1000.) 

The  advantages  of  monolithic  and  reinforced  concrete 
over  all  other  forms  of  construction  in  foundations  are  seen 

328 


in  structures  resting  on  yielding  soils.  The  solid  mass  of 
concrete,  as  in  a  wall,  tends  to  settle  as  a  unit,  and  uni- 
formly, even  though  the  pressure  may  not  be  quite  uniform 
on  the  entire  foundation. 

Lateral  flow  in  the  subsoil  is  especially  troublesome  in 
soils  of  a  clayey  nature  or  in  sand  that  is  saturated  with 
water.  Quicksand  is  a  saturated  sand  that  flows  very  free- 
ly, but  many  saturated  sands  that  would  not  be  classed 
as  quicksands  are  subject  to  this  lateral  flow;  and  founda- 
tions upon  such  require  the  utmost  care.  A  good  precau- 
tion is  to  drive  sheet  piling  just  outside  of  the  foundation. 
so  as  to  retain  the  sand  or  other  soil,  if  flowing  is  antici- 
pated. This  will  greatly  increase  the  bearing  power.  The 
tower  of  the  Hamburg  water  works  is  about  290  ft.  high. 
It  is  built  of  brickwork  and  rests  on  a  circular  block  of 
concrete  56  ft.  in  diameter  and  n  ft.  thick.  This  rests  on 
quicksand  enclosed  by  sheet  piling  driven  below  the  line  of 
saturation  of  the  River  Elbe.  The  pressure  is  about  2  tons 
per  sq.  ft.  on  the  quicksand. 

Much  trouble  is  caused  in  the  city  of  Chicago  due  to  the 
flowing  of  the  subsoil.  In  the  down-town  portions  of  the 
city  there  is  first  a  layer  of  about  13  ft.  of  made  ground, 
then  6  to  12  ft.  of  a  hard  clay,  below  which  is  a  softer 
clay  for  about  60  or  80  ft.  to  rock  or  hardpan.  In  some 
places  this  clay  becomes  very  hard  towards  the  rock  and 
contains  large  boulders.  Before  the  days  of  tall  buildings 
foundations  in  Chicago  were  generally  laid  on  top  of  the 
crust  of  stiff,  blue  clay  found  about  13  feet  below  the  sur- 
face. This  was  loaded  with  about  1 24  to  2  tons  per  sq.  ft., 
and  in  order  to  get  the  necessary  area  in  contact  spread 
footings  were  employed.  These  are  large  pyramids  that 
had  to  rest  on  top  of  the  hard  clay,  as  it  was  found  that 
the  bearing  power  was  less  if  they  penetrated  into  the  clay. 
Before  building  the  Masonic  Temple  the  soil  was 
tested  by  a  tank  having  an  area  of  2  sq.  ft.  in 
contact  with  the  soil.  This  was  loaded  until  the 
pressure  was  5,650  Ib.  per  sq.  ft.  In  one  test  it 
was  placed  on  top  of  the  hard  clay  for  100  hours;  the 


settlement  was  I  13-16  in.  In  a  second  test  it  was  sup- 
ported at  the  bottom  of  a  hole  2  ft.  4  in.  deep  in  the  hard 
clay;  the  settlement  was  4l/&  in. 

Some  of  the  taller  buildings  were  founded  on  these 
spread  footings,  but  it  was  found  that  the  entire  crust 
was  depressed  by  the  great  load.  The  settlement  was  great- 
er, though  the  unit  pressure  was  the  same  as  in  smaller 
buildings.  This  was  especially  the  case  where  any  exca- 
vation was  made  below  the  crust  in  the  neighborhood  of 
these  buildings.  Excavation  for  the  freight  tunnels,  which 
are  about  40  ft.  under  ground,  recently  caused  some  tall 
buildings  to  settle  and  develop  bad  cracks  on  account  of 
the  flowing  of  the  soil. 

The  present  methods  of  sinking  foundations  in  Chicago 
will  be  described  later.  Even  these  cause  some  settlement 
in  old  buildings  because  of  unavoidable  spaces  left  around 
the  lagging  in  the  wells. 

Sometimes  retaining  walls  are  built  around  the  site  of 
a  building  below  grade.  This,  however,  is  to  prevent  the 
flowing  in  of  the  soil,  if  excavation  is  made  for  a  sub- 
basement 

The  bearing  power  of  gravel  or  other  similar  material 
may  sometimes  be  greatly  increased  by  the  use  of  grout. 
Gravel  not  mixed  with  sand  may  readily  be  consolidated 
into  a  sort  of  concrete  by  forcing  into  the  interstices  cement 
grout.  This  has  been  done  also  where  some  sand  was 
present  in  the  gravel,  by  first  pumping  out  some  of  the 
sand.  The  first  method  was  employed  in  the  foundation 
of  a  bridge  over  the  Danube,  near  Ehingen,  Wuerttemberg. 
Pipes  having  loosely  inserted  driving  points  were  driven 
into  the  gravel  at  intervals  of  18  or  20  in.  By  drawing 
the  pipe  up  a  few  inches  to  clear  the  point  grout  could 
be  pumped  into  the  gravel.  Then  by  successive  withdrawals 
and  pumpings  a  concrete  was  made  of  the  natural  gravel  in 
place.  The  gravel  was  one  which  contained  running  water 
and  little  sand.  This  would  not  work  in  sand  or  in  gravel 
where  much  sand  is  present.  (See  Eng.  News,  Jan.  9, 
1902.) 

330 


By  the  same  means  a  sort  of  cofferdam  can  be  made  in 
gravel  by  sinking  the  pipes  around  the  site  of  the  proposed 
excavation  and  building  up  a  wall  inside  of  which  ex- 
cavation can  be  made. 

There  is  a  process  (patented  Dec.  8,  1891)  for  injecting 
cement  grout  into  quicksand  in  the  making  of  a  foundation 
in  the  same.  It  consists  of  (i)  sinking  pipes  into  the 
sand,  (2)  pumping  out  the  sand  so  as  to  leave  a  chamber, 
(3)  forcing  cement  grout  into  this  chamber.  (See  Eng. 
News,  April  28,  1892;  June  28,  1894;  Oct.  16,  1902.)  One 
way  to  get  out  the  sand  is  to  use  two  pipes  near  together, 
forcing  water  into  one  while  the  water  and  sand  are  being 
pumped  out  of  the  other. 

In  the  foundation  work  of  the  Merrimac  River  bridge 
at  Newburyport,  Mass.,  cylindrical  piers  were  sunk  by 
open  dredging  to  a  level  where  rock  was  indicated  by  the 
borings,  and  the  bottom  was  found  to  consist  of  boulders 
in  a  stratum  of  coarse  sand  and  gravel.  The  cylinders 
were  then  converted  into  pneumatic  caissons,  with  air  locks 
placed  on  top,  and  were  loaded  with  pig  iron.  The  water 
in  them  was  then  blown  out.  No  rock  ledge  was  found 
within  reach  of  steel  probing  rods  12  ft.  long,  and  it  was 
decided  to  use  the  boulders  and  gravel  as" the  foundation. 
A  foot  or  more  of  water  was  allowed  to  rise  in  the  cylinder, 
and  Portland  cement  was  mixed  with  it  and  kept  well 
stirred.  By  increasing  the  air  pressure  this  grout  was 
forced  out  into  the  surrounding  gravel  and  boulders.  The 
mass  was  thus  rendered  stronger  to  receive  the  founda- 
tion. (See  Engineering  Record,  Vol.  50,  page  220.) 

When  soil  is  deemed  too  soft  to  support  the  weight  of 
a  structure,  piles  are  sometimes  driven  in.  These  support 
the  weight  either  by  virtue  of  their  penetrating  to  hard 
bottom  or  by  friction  on  the  surrounding  soil.  Where  a 
substratum  of  rock  can  be  reached,  the  piles  should  be 
driven  to  the  same,  and  driving  should  cease  as  soon  as 
this  is  reached.  Further  hammering  may  broom  or  split 
the  pile  or  cause  it  to  fail  by  diagonal  shear  and  thus 
destroy  its  usefulness.  There  are  various  rules  for  de- 

331 


termining  when  sufficient  hammering  has  been  done.  One 
rule  allows  a  penetration  not  over  16  in.  in  the  last  ten 
blows  of  a  2,6oo-lb.  hammer  falling  15  ft.  Another  rule 
allows  a  penetration  not  over  I  in.  in  the  last  blow  with 
a  2,ooo-lb.  hammer  falling  10  ft.  Another  allows  a  pene- 
tration not  over  3  in.  under  a  2,ooo-lb.  hammer  falling  15  ft. 
for  piles  supported  by  friction  only.  One  rule  for  piles 
driven  with  a  steam  hammer,  the  hammer  of  which  weighs 
5,000  lb.,  requires  that  the  piles  will  not  move  more  than 
J4  in.  to  the  blow,  when  driving  is  complete. 

By  the  New  York  Building  Code  piles  intended  to  sustain 
a  wall,  pier,  or  post  must  be  spaced  not  more  than  36  or 
less  than  29  in.  in  centers.  They  must  be  driven  to  a  solid 
bearing  if  practicable  to  do  so.  Piles  less  than  20  ft.  in 
length  may  be  5  in.  at  the  small  end  and  10  in.  at  the  butt. 
Piles  more  than  20  ft.  in  length  must  not  be  less  than  12 
in.  at  the  butt.  The  maximum  load  allowed  per  pile  is 
20  tons. 

A  rule  quite  general  in  Boston  is  to  allow  a  safe  load 
of  10  tons  per  pile  when  supported  by  friction.  Piles 
reaching  hard  stratum  may  be  loaded  to  16  tons.  (See 
Eng.  News,  February  5,  1903). 

Specifications  for  bridges  in  the  city  of  Milwaukee  allow 
a  load  of  12  tons  on  each  pile.  Piles  must  be  not  less 
than  14  in.  at  butt  and  9  in.  at  small  end  and  55  ft.  long, 
driven  to  hard  bottom.  The  minimum  spacing  is  2  ft.  on 
centers.  Piles  may  be  of  pine,  tamarack,  or  hemlock. 

The  "Engineering  News  Formula"  for  the  safe  load  on 
piles  allows  a  load  in  tons  equal  to  twice  the  weight  of 
hammer  in  tons  times  fall  in  feet  divided  by  one  plus 
penetration  of  pile  under  last  blow,  in  inches. 

To  prevent  the  splitting  of  the  head  of  a  pile  a  steel  ring 
about  3  in.  wide  and  l/2  in.  or  more  thick  and  about  the 
diameter  of  the  head  is  laid  on  it  and  driven  into  the 
fibers  with  the  hammer.  This  is  pulled  off  by.  means  of  a 
tool  for  the  purpose  when  the  driving  is  completed.  Where 
one  piece  of  timber  will  not  reach  to  the  required  depth,  it 
is  sawed  off  and  spliced  by  means  of  a  dowel  and  side 
332 


straps  of  wood  or  iron.  Piles  are  usually  sharpened  with 
a  blunt  point.  Sometimes  steel  straps  are  laid  across  the 
point  two  ways  and  spiked  on,  and  sometimes  cast  iron 
shoes  are  used  to  facilitate  the  penetration  and  to  protect 
the  pile. 

Timber  piles  in  permanent  structures  should  only  be 
used  where  always  wet.  The  piles  are  usually  sawed  off  at 
an  even  level,  below  low  water  line,  and  the  earth  is  ex- 
cavated around  them  for  2  ft.  or  more.  This  is  then  filled 
with  concrete  and  the  pier  footing  of  concrete  laid  upon 
the  same.  Care  must  be  taken  in  laying  masonry  upon  the 
concrete  to  see  that  it  is  set  first. 

Cheap  woods,  such  as  spruce  and  hemlock,  are  generally 
used  for  piles  completely  under  water,  as  they  will  last 
indefinitely  if  kept  from  contact  with  the  air.  These  soft 
woods  can  be  obtained  in  lengths  from  20  to  50  ft.  and 
diameters  10  to  12  in.  at  the  head.  Hard  pine  piles  can 
be  obtained  up  to  75  or  80  ft.  in  length  with  diameters  at 
the  head  of  about  16  in. 

Concrete  piles  have  recently  come  into  extended  use. 
These  may  be  made  by  filling  up  with  concrete  the  hole 
left  by  a  pile  of  wood  or  metal.  In  some  a  sheet  metal  shell 
covering  a  removable  wooden  core  is  driven  into  the  ground 
and  then  the  core  withdrawn  and  the  shell  filled  with 
concrete.  These  are  often  tapered.  They  are  generally 
of  larger  diameter  than  wooden  piles. 

The  following  method  was  employed  in  some  concrete 
pile  work  at  Pittsburg  in  1904.  Steel  tubes  about  16  in, 
in  diameter,  of  metal  about  $i  in.  thick,  having  bullet 
shaped  shoes  loosely  inserted  in  the  ends  and  with  wooden 
heads,  were  driven  into  the  ground  by  means  of  pile 
drivers.  Where  the  ground  was  hard,  these  shoes  were  of 
cast  iron;  and  where  sufficiently  soft,  they  were  of  con- 
crete previously  made  and  allowed  to  harden.  When 
driven  to  the  required  depth,  the  tube  was  drawn  up  a 
little;  and  a  rammer,  made  of  long  cast  iron  weight  sus- 
pended on  a  rope,  was  let  into  the  inside.  The  known 
length  of  the  line  supporting  this  rammer  served  to  in- 


dicate  whether  the  shoe  was  in  the  proper  place  (not  being 
drawn  up  by  the  tube)  ;  or,  if  a  concrete  shoe  had  been 
used,  it  would  show  whether  it  had  remained  whole  and 
had  not  been  jammed  up  into  the  tube.  Concrete  buckets 
made  of  old  house  boilers  were  then  filled  and  the  concrete 
deposited  into  the  tubes  through  gates  in  the  bottom  of 
these  buckets.  After  each  bucketful  had  been  deposited 
and  rammed  the  tube  was  drawn  up  a  little  further,  the 
distance  being  gauged  by  a  mark  on  the  line  suspending 
the  rammer.  The  buckets  were  not  let  into  the  tube,  but 
were  emptied  at  the  upper  end  of  the  same.  Parts  of  this 
process  are  patented. 

Piles  reinforced  with  steel  are  sometimes  molded  at  the 
site,  and  after  setting  and  hardening  are  driven  in  the  same 
manner  as  wooden  piles.  A  method  of  protecting  the  head 
of  such  a  pile  in  driving  is  described  in  Eng.  News,  De- 
cember 27,  1906.  It  consisted  in  a  steel  tube  fitting  over 
the  top  of  the  pile  and  having  a  diaphragm  against  which 
on  one  side  was  a  long  wooden  block  to  receive  the  blows 
and  on  the  other  side  a  short  wooden  block,  and  between 
this  and  the  head  of  the  pile  a  cushion  of  rope. 

The  foundations  of  tall  buildings  in  Chicago  are  now 
generally  made  on  what  might  be  called  concrete  piles. 
They  vary  from  3  to  12  ft.  in  diameter  and  are  sometimes 
100  ft.  long  or  more,  reaching  down  to  hardpan  or  solid 
rock.  The  excavation  is  done  by  hand  in  depths  of  4  or 
5  ft.  at  a  time.  This  circular  hole  is  sheathed  with  vertical 
lagging  made  of  boards  2  or  3  in.  thick  planed  radially  on 
the  edges  and  fitted  tightly  together.  These  are  held  in 
place  by  flat  steel  bands,  segmental  in  shape  and  flanged 
on  the  ends,  bolted  together  to  form  a  complete  circle. 
Then  the  excavation  is  made  another  4  or  5  ft.,  and  this 
is  also  surrounded  by  lagging.  At  the  bottom,  if  the  pile 
is  to  rest  on  hardpan,  the  well  is  belled  out  to  twice  the 
diameter.  The  piles  are  generally  loaded  to  about  20  tons 
per  sq.  ft.,  and  this  would  give  a  load  of  5  tons  per  sq.  ft. 
on  the  hardpan.  The  holes  or  wells  are  filled  wth  con- 
crete, well  tamped,  which  should  preferably  be  let  down 

334 


in  buckets,  so  as  not  to  separate  the  ingredients  and  thus 
impair  the  uniformity  of  the  concrete.  Sometimes  the 
lagging  is  left  in  place,  and  sometimes  it  is  removed  as 
the  concreting  progresses.  The  concrete  is  best  made  of 
a  mixture  of  i  Portland  cement  to  2  sand  to  4  broken 
stone  or  gravel.  Sometimes  1 13 :5  concrete  is  used.  Where 
a  pocket  of  quicksand  is  encountered,  it  is  apt  to  flow 
into  the  well  and  to  make  a  change  in  the  method  of  ex- 
cavation necessary.  One  method  of  meeting  the  difficulty 
is  to  use  a  steel  cylinder,  in  segments  bolted  together,  either 
allowing  it  to  sink  as  the  excavation  progresses  or  forcing 
it  down  with  jacks.  This  is  not  always  successful,  and 
resort  must  be  had  to  the  use  of  sheet  piling  driven  from 
the  surface  through  the  stratum  of  quicksand.  Thus  a 
sort  of  cofferdam  is  made  around  the  well  inside  of  which 
excavation  can  be  done  without  difficulty.  When  the  sand 
is  penetrated,  the  first  described  method,  using  short  lag- 
ging, is  resumed.  Steel  sheet  piling  is  best  for  the  purpose, 
as  it  will  penetrate  further  wthout  injury,  and  it  can  be 
drawn  and  used  again. 

The  tops  of  these  concrete  shafts  are  capped  with  grillage 
beams  or  other  means  of  distributing  the  load  of  the 
column  uniformly  over  the  concrete. 

The  load  allowed  on  concrete  piles  should  not  exceed 
20  tons  per  sq.  ft.  for  those  of  large  diameter.  If  there 
is  any  possibility  of  their  acting  as  columns,  as  in  the  event 
of  the  surrounding  earth  being  removed,  the  unit  load 
should  be  less.  Concrete  is  weak  in  columns,  unless  it  is 
properly  reinforced  with  steel.  A  better  load  on  piles  of 
small  diameter  is  about  15  tons  per  sq.  ft. 

Screw  piles  are  sometimes  made  use  of  to  distribute 
pressure  and  to  anchor  structures  such  as  lighthouses,  sig- 
nal towers,  etc.  They  are  made  of  a  shaft  of  steel  or  cast 
iron  and  an  auger  shaped  blade  of  about  one  turn.  They 
are  driven  in  by  turning  either  by  hand  or  other  power. 
Screw  piles  for  supporting  parts  of  the  tunel  for  the  Penn- 
sylvania and  Long  Island  R.  R.  under  the  Hudson  River 
are  to  be  made  of  cast  iron  in  7  ft.  sections,  having  inside 

335 


flanges  at  splice  which  take  4  i*A  in.  bolts  and  12  steel 
dowels.  The  piles  are  27  in.  outside  diameter  and  of  i^ 
in.  metal,  and  the  diameter  of  the  screw  is  4  ft.  8  in.  They 
are  spaced  15  ft.  and  aid  in  the  support  of  a  single  track 
tunnel.  (See  Eng.  News,  Oct.  12,  1903.) 

The  load  coming  upon  the  soil  of  a  foundation  or  on  a 
system  of  piles  consists  of  the  total  dead  load  carried  and 
some  or  all  of  the  nominal  live  or  superimposed  load  that 
the  structure  may  be  called  upon  to  carry.  In  tall  build- 
ings it  is  not  necessary  to  include  all  of  the  live  load,  as 
the  floors  are  never  all  fully  loaded  with  the  calculated 
capacity.  The  New  York  Building  Code  allows  a  reduc- 
tion in  column  loads  of  5  per  cent  of  the  live  load  of  2 
floors  (including  the  roof)  ;  10  per  cent  of  the  live  load  of 
3  floors;  15  per  cent  of  4  floors;  down  to  50  per  cent  of  n 
floors,  and  50  per  cent  reduction  for  any  more  than  n 
floors. 

In  estimating  the  weight  on  a  foundation  part  of  which 
is  permanently  under  water  ft  is  legitimate  to  deduct  the 
buoyancy  of  the  water  for  the  part  of  the  foundation  that 
is  below  low  water  line.  Thus  in  piers  at  Chicago  and 
Milwaukee  62.5  Ibs.  per  cu.  ft.  of  masonry  below  water 
level  may  be  deducted  from  the  weight  of  piers.  On  the 
other  hand  this  same  deduction  should  be  made  in  de- 
termining the  stability  of  a  partly  submerged  pier  used  as 
an  anchor  against  uplift  or  horizontal  forces. 

A  brief  description  of  the  processes  used  in  excavating 
for  foundations  will  be  in  place  here.  The  ordinary  proc- 
ess of  excavating  for  foundations  where  water  is  not  en- 
countered is  simple  and  the  problems  are  few.  Apart  from 
digging  or  blasting  out  the  material  and  handling  the 
same  there  is  often  the  question  of  shoring  up  the  sides 
against  a  cave-in.  In  a  wide  excavation  in  loose  ground 
the  shores  should  not  be  merely  horizontal  struts,  but  these 
struts  should  be  braced  together  diagonally  and  vertically 
to  prevent  displacement.  Wedges  or  jacks  should  be  used 
to  give  a  firm  bearing  against  the  earth,  as  it  is  much 


easier  to  prevent  earth  from  sliding  than  to  stop  it  when 
it  has  once  loosened  and  started  to  slide. 

There  is  a  process  of  excavating  through  flowing  soils 
known  as  the  freezing  process.  It  is  expensive  and  not 
used  very  much.  It  consists  of  forcing  into  the  soil  just 
outside  of  the  opening  to  be  made  refrigerating  pipes 
freezing  the  mass,  excavating  and  then  damming  off  the 
soil  or  building  in  the  stone  or  concrete  work. 

There  are  three  methods  of  excavating  for  foundations 
in  water.  One  is  by  making  a  cofferdam  by  driving  sheet 
piling  around  the  space  to  be  excavated  and  digging  out 
the  earth.  The  water  is  kept  pumped  out  as  the  excava- 
tion proceeds.  Wooden  sheet  piling,  called  Wakefield  pil- 
ing, consists  of  boards  spiked  and  bolted  together  in  threes, 
the  middle  one  being  set  back  to  form  a  tongue  at  one 
side  and  a  groove  at  the  other.  Steel  sheet  piling  has  been 
found  to  be  very  useful  for  cofferdam  work.  It  has  greater 
strength  than  wooden  piling,  and  there  is  less  leakage. 
The  piles  can  be  used  repeatedly.  Sometimes  they  rust 
together  in  the  ground.  A  blow  from  the  pile  driver  on 
the  head  of  one  pile  will  generally  loosen  the  one  to  be 
drawn. 

A  second  method  is  called  open  dredging.  This  consists 
in  dredging  out  the  earth  in  the  inside  of  a  casing,  which 
sinks  as  the  earth  is  removed.  The  casing  forms  a  shell 
for  the  pier,  being  filled  with  concrete  when  sunk  to  the  de- 
sired depth.  The  shell  has  a  uniform  outside  diameter  and 
is  tapered  from  the  inside  to  a  cutting  edge.  The  dredging 
is  done  by  means  of  steam  shovels,  or  clam  shell,  orange 
peel  or  other  bucket  dredges. 

Hydraulic  dredging,  used  in  different  methods  of  ex- 
cavation, is  done  by  means  of  pumps.  Where  loose  ma- 
terials are  to  be  removed  by  pumping  out,  a  jet  of  water 
agitating  the  materials  will  cause  them  to  be  drawn  up 
by  the  pump.  Jets  of  water  may  be  used  to  advantage  in 
open  dredging  to  loosen  the  soil  under  the  cutting  edge. 
Sometimes  the  cutting  edge  encounters  boulders  which 

337 


the  dredge  will  not  remove,  and  it  is  necessary  to   send 
down  divers  to  remove  the  same. 

By  use  of  the  open  dredging  process  in  the  foundation 
of  the  Atchafalaya  Bridge  at  Morgan  City,  La.,  the  depth 
of  foundation  bed  was  made  about  120  ft.  below  high  water 
and  70  to  115  ft.  below  the  silt  or  mud  surface.  The 
greatest  depth  attained  by  this  method  in  a  bridge 
foundation  was  reached  in  sinking  the  piers  of  the  Hawkes- 
bury  Bridge  in  Australia,  namely,  about  170  ft.  below  water 
or  126  ft.  below  the  river  bed. 

Concrete  deposited  in  deep  water,  as  in  an  excavation 
made  by  open  dredging,  is  apt  to  have  the  cement  washed 
out.  To  overcome  this  it  may  be  dropped  through  a  tube 
or  a  tremie  in  as  large  loads  as  practicable.  If  put  into 
jute  bags,  the  cement  will  be  retained;  enough  cement  will 
ooze  out  of  the  meshes  to  cement  the  pieces  together. 
Concrete  mixed  extra  long  or  even  retempered  concrete, 
if  it  has  not  stood  too  long,  is  preferable  to  concrete  in 
which  the  cement  is  too  freshly  mixed,  where  it  is  to  be 
deposited  in  water. 

The  other  method  of  excavation  is  the  pneumatic  process. 
An  airtight  timber  crib  or  caisson  is  made,  having  a  space 
underneath  large  enough  for  men  to  work  in,  provided 
with  a  cutting  edge  around  the  periphery  and  supplied  with 
air  locks,  etc.,  in  the  roof.  This  is  placed  in  the  position 
which  the  pier  is  to  occupy  and  allowed  to  rest  upon  the 
ground.  Men  enter  and  leave  through  the  air  locks,  and 
the  excavated  earth  is  hauled  up  in  buckets  through  locks 
for  the  purpose.  Air  is  continuously  pumped  in  and  it 
escapes  below  the  cutting  edge.  Ordinarily  this  air  pres- 
sure keeps  the  water  out,  but  if  the  soil  becomes  dense  or 
is  clayey,  the  air  pressure  can  often  be  reduced  below  the 
hydraulic  head  of  the  cutting  edge,  greatly  to  the  benefit 
of  the  workmen.  In  such  case  the  water  that  leaks  in  may 
be  removed  with  an  ejector. 

As  the  crib  sinks  the  pier  is  built  on  it,  and  when  suit- 
able bottom  is  reached  the  working  chamber  is  filled  with 
concrete. 


In  the  Brooklyn  pier  of  the  new  East  River  Bridge  a 
depth  of  115  ft.  below  high  water  was  reached  by  the 
pneumatic  process.  In  a  bridge  over  the  Barrow  River  in 
'Ireland  a  depth  of  127  ft.  below  high  water  was  reached. 
In  this  work  the  air  pressure  used  was  42  to  45  Ib.  at  the 
maximum  depth.  (See  Eng.  News,  Vol.  53,  p.  607). 

In  foundations  for  tall  buildings  in  New  York  some- 
times pneumatic  caissons  are  required.  These  are  sunk 
under  the  individual  columns  or  under  two  or  more  col- 
umns in  a  group.  (See  Eng.  Record,  Sept.  3,  1904,  for 
description  of  caissons  under  Trinity  Building.) 

The  second  requisite  of  a  good  foundation,  namely,  a 
uniform  unit  pressure  on  the  entire  foundation,  has  special 
force  in  foundations  on  soft  soil.  On  such  soils  there 
will  be  some  settlement,  and  if  the  unit  pressure  is  greater 
at  one  point  than  another,  settlement  will  be  greater  at 
that  point.  This  condition  of  uniform  pressure  is  effected 
by  making  the  area  in  bearing  on  the  soil  in  proportion  to 
the  load  to  be  carried.  A  great  part  of  the  settlement  of 
a  building  takes  place  during  erection,  and  it  is  hence  due 
to  the  dead  weight  in  greater  measure  than  to  the  super- 
imposed weight.  In  any  event,  as  only  a  part  of  the  super- 
imposed load  is  on  the  floors  continuously,  the  dead  load 
must  be  taken  as  the  prime  factor  in  determining  the  size 
of  footings.  If  the  footings  of  all  of  the  columns  of  a 
building  were  given  areas  in  proportion  to  the  total  dead 
and  live  load  to  be  carried,  those  carrying  the  walls  would 
settle  more  than  the  interior  columns.  However,  the  areas 
of  the  footings  for  the  interior  columns  should  be  based 
on  the  probable  maximum  load,  so  that  the  safe  pressure 
on  the  soil -is  not  exceeded. 

Sometimes  the  density  of  the  soil  varies  under  different 
parts  of  a  building.  In  such  case  the  foundation  should 
be  proportioned  so  that  the  pressure  will  be  in  conformity 
to  the  bearing  power  of  the  soil  at  different  parts.  The 
leaning  tower  of  Pisa  seems  to  have  acquired  the  lean 
which  has  made  it  famous  by  uneven  settling  on  soils  of 
different  densities. 

339 


Eccentrically  loaded  piers  resting  on  piles  should  have 
\he  center  of  gravity  of  the  system  of  piles  coinciding  with 
that  of  the  load  as  near  as  practicable. 

The  third  requisite,  namely  the  maintenance  of  a  posi- 
tive pressure  on  the  soil  at  all  parts,  has  special  force  as 
applied  to  foundations  for  high  or  narrow  structures  where 
the  wind  may  cause  tension  or  uplift  on  the  windward  side 
at  the  edge  of  foundation,  also  for  anchorages  of  cantilever 
or  suspension  bridges. 

In  order  to  have  no  tension  on  the  extreme  edge  of  a 
rectangle,  the  resultant  of  the  vertical  load  and  the  hori- 
zontal force  (as  the  wind  load  or  pull  of  anchorage)  must 
fall  within  the  middle  third  of  the  base.  In  a  circular  sec- 
tion the  resultant  should  fall  within  the  middle  quarter  of 
the  base.  This  is  a  condition  which  follows  upon  the 
theory  of  flexure.  It  does  not  mean  that  there  is  a  factor 
fef  safety  of  three  when  the  resultant  falls  within  the 
middle  third  of  the  base.  It  simply  means  that  this  condi- 
tion must  hold,  if  there  is  to  be  no  tension  and  no  tendency 
to  rise,  at  any  part  of  the  base.  In  a  material  incapable 
Sof  taking  any  tension,  or  nearly  so,  such  as  a  wall  resting 
bn  the  soil,  or  a  wall  laid  in  lime  mortar,  there  should  be 
absolutely  no  tension  or  tendency  to  rise  anywhere.  Such 
tendency  would  be  detrimental  to  the  safety  of  the  struc- 
ture, especially  if  it  be  a  reversible  condition,  as,  for  ex- 
ample, in  a  tower  where  joints  may  tend  to  open  on  one 
side  and  then  on  the  other,  due  to  reversal  of  the  wind. 
Of  course  it  is  true  that  one  application  of  the  wind  load 
would  not  overturn  the  tower,  if  the  resultant  fell  some- 
where between  the  middle  third  and  the  outer  edge,  as  the 
resultant  must  fall  without  the  base  in  order  to  overturn 
a  body.  But  the  racking  will  loosen  the  joints  and  tend 
ultimately  to  ruin  the  walls.  In  a  foundation  it  is  manifest 
that  any  such  disturbance  in  the  region  of  the  main  sup- 
porting medium  of  a  structure  would  be  harmful. 

The  condition  requiring  that  the  resultant  fall  within 
the  middle  third  of  the  base  may  be  seen  from  another 
standpoint,  namely,  that  of  uniformly  varying  pressures. 
340 


Suppose  the  resultant  pressure  falls  in  the  middle  of  the 
base  of  a  foundation  as  at  (a),  Fig.  i.  The  reaction  of 
the  soil  will  be  uniform  across  the  width  of  the  base,  as 
represented  by  the  row  of  short  arrows.  If  the  resultant 
of  the  pressure  falls  1-3  of  the  base  from  the  edge  of  the 
same  as  at  (b),  the  reaction  will  be  greatest  in  intensity 
at  the  edge  nearest  this  resultant,  and  it  is  necessary  that 
the  center  of  gravity  of  this  reaction  be  on  the  line  of  the 
resultant.  Again,  if  the  reacting  medium  be  yielding  or 
elastic,  the  pressure  will  vary  uniformly  from  the  maxi- 
mum at  the  right  edge  of  the  base  to  a  minimum  at  the  left 
edge.  Only  a  triangle,  as  indicated  in  the  figure,  can 
fulfill  these  conditions.  Hence  the  pressure  varies  from 
zero  at  the  left  edge  to  an  intensity  double  the  mean  pres- 
sure at  the  right  edge. 

If  the  resultant  is  closer  to  one  edge  than  1-3  of  the 
base,  and  the  variation  of  pressure  is  uniform,  one  of  two 
things  must  occur;  either  there  will  be  tension  on  the 
farther  edge,  or  the  pressure  will  be  zero  for  whatever 
width  of  base  remains  in  excess  of  3*  [See  Fig.  i,  at  (c)]. 
A  floating  rectangular  block  supporting  an  eccentric  load 
whose  resultant,  or  center  of  gravity,  falls  closer  than  1-3 
of  the  width  from  the  edge  would  be  out  of  water  for  the 
width  of  block  exceeding  3^:. 

Fig.  2  shows  the  anchorage  of  a  suspension  bridge.  The 
force  A  B  is  the  pull  on  the  cable;  A  C  represents  the 
weight  of  the  anchor  pier,  applied  at  the  center  of  gravity 
of  the  pier;  A  D  is  the  resultant.  This  latter  force  should 
pass  within  the  middle  third  of  the  base 

Fig.  3  shows  the  pier  for  a  trunnion  bridge,  such  as  the 
bascule  bridges  of  which  a  number  are  found  in  the  city 
of  Milwaukee.  The  force  A  is  the  total  dead  load  of 
trunnion  and  approach  girders.  This  will  be  at  the  center 
of  column  supporting  these  loads,  as  the  trunnion  girders 
are  counterbalanced  for  dead  load.  The  force  B  is  the 
dead  weight  of  the  pier,  allowance  being  made  for  the 
buoyancy  of  the  water.  C  is  the  sum  of  the  live  load  over- 
hanging the  pier.  The  resultant  of  all  of  these  is  in  amount 
341 


342 


equal  to  the  sum  of  the  three.  Its  position  is  found  by 
taking  moments,  say  around  the  edge  of  the  pier.  It  is 
preferable  that  this  resultant  fall  within  the  middle  third 
of  the  base,  but  if  the  pier  is  founded  on  piles,  they  may 
be  driven  closer  on  the  side  of  the  higher  pressure,  thus 
allowing  the  resultant  to  fall  closer  to  that  edge. 

In  the  foundation  of  a  chimney  or  tower  the  same  prin- 
ciples apply.  The  dead  weight  of  the  structure  is  one  force 
always  present,  and  the  greatest  possible  wind  load  is  to 
be  combined  with  the  same.  The  direction  of  this  result- 
ant must  be  such  as  to  pass  within  the  middle  third  in 
the  case  of  a  rectangular  base  or  within  the  middle  quarter 
in  the  case  of  a  circular  base,  that  is,  it  must  fall  not  over 
1-6  or  1-8  of  the  diameter  of  the  bases  respectively,  from 
the  center. 

It  is  legitimate  to  allow  somewhat  greater  pressure  at 
the  edge  of  a  foundation  than  those  given  heretofore, 
where  the  increase  is  due  to  the  maximum  wind  load.  An 
increase  of  25  per  cent  over  the  unit  regularly  allowed 
would  be  a  reasonable  allowance  at  the  edge  where  the 
pressure  is  of  maximum  intensity. 

The  fourth  requisite  would  demand  that  foundations  be 
made  deep  enough  to  be  free  from  danger  of  undermining 
by  abrasion  from  streams  or  drainage  water,  or  by  ex- 
cavation for  foundations  of  adjacent  structures.  They 
should  be  deep  enough  to  rest  on  soil  not  affected  by  frost. 

Many  failures  of  bridges  have  been  due  to  the  washing 
away  of  the  soil  beneath  the  piers.  Gravel  beds,  upon 
which  piers  often  rest,  could  very  often  be  cemented  to 
advantage  into  one  mass  by  the  use  of  grout,  as  herein- 
before described.  Often  the  scouring  action  of  the  stream 
will  carry  away  large  stones  of  the  piers  themselves.  These 
stones  lose  nearly  half  their  weight  when  submerged,  and ; 
are  hence  comparatively  easy  to  move.  This  is  a  strong 
argument  for  solid  concrete  piers. 

A  depth  of  4  or  5  ft.  is  sufficient  to  reach  soil  not  af- 
fected by  frost  in  temperate  regions.  This  is  deep  enough 


for  light  foundations  as  for  mill  buildings,  etc.,  where  the 
soil  is  not  made  ground  or  fill. 

The  fifth  requisite  of  a  good  foundation,  namely,  that  the 
materials  be  practically  indestructible  in  their  respective 
places,  can  be  assured  only  by  using  materials  of  known 
lasting  qualities.  Brick  should  not  be  used  in  sea  water. 
Wood  should  be  used  only  where  it  will  be  always  under 
water  or  always  exposed  to  air  only.  Cement  mortar  and 
not  lime  mortar  should  be  used  in  wet  places,  as  lime 
mortar  requires  a  long  time  to  harden  if  kept  wet.  Steel 
placed  in  concrete  is  probably  better  not  painted,  as  the 
concrete  will  adhere  better  to  the  steel  than  to  the  paint 
I  and  is  a  better  medium  of  protection  than  paint. 

The  sixth  requisite  demands  a  foundation  that  is  strong 
enough  to  do  the  work  that  it  may  be  called  upon  to  do. 
The  forces  to  be  resisted  may  be  (i)  a  downward  force 
due  to  the  weight  of  the  structure  carried,  (2)  an  upward 
force  due  to  an  uplift  that  may  be  exerted  upon  the  foun- 
idation,  (3)  horizontal  or  overturning  forces,  (4)  the  up- 
ward reaction  of  the  supporting  soil. 

The  base  of  a  steel  or  cast  iron  column  or  a  bridge  bolster 
;<>r  shoe  resting  on  stone  or  other  masonry  should  have 
sufficient  area  in  contact  with  the  stone  to  prevent  crush- 
iing.  It  should  be  borne  in  mind  that  generally  such 
ibases  do  not  have  an  ideal  bearing,  so  that  the  unit  em- 
jployed  should  be  low,  that  is,  a  large  factor  of  safety 
(should  be  used  It  is  true  that  building  columns  and  some 
(other  bases  are  often  set  up  a  little  above  the  surface  of 
[the  stone  or  concrete  and  the  space  filled  in  with  grout,  but 
lit  is  also  true  that  bridge  seats  are  very  often  placed  directly 
on  the  surface  of  the  stone.  The  following  are  good  units 
of  safe  pressure  to  allow  on  various  classes  of  masonry, 
in  Ib.  per  sq.  in.:  Brick  masonry  in  lime  mortar,  150; 
brick  masonry  in  cement  mortar,  200;  ordinary  rubble 
masonry,  200;  good  bridge  masonry,  250;  granite,  400. 

It  is  of  great  importance  that  the  masonry  pier  receiving 
a  cast  column  base  be  a  rigid  mass  under  the  base.     The 
writer  observed  a  number  of  cast  column  bases  on  rubble 
344 


piers  that  were  split  in  two  by  the  weight  of  the  column,  j 
The  rubble  appeared  to  sink  under  the  center  of  the  column  j 
leaving  the  cast  base  supported  on  its  edges.     Not  being 
suited  to  take  such  a  heavy  bending  moment  the  cast  base 
broke  under  the  weight.     The  cap  of  a  pedestal  or  pier 
taking  a  column  should  be  a  single  stone,  or,  better,  the 
entire  pier  should  be  a  monolith  of  concrete. 

A  large  building  in  Pittsburg  collapsed  some  years  ago 
on  account  of  the  fact  that  a  brick  wall  between  two  build- 
ings that  were  being  thrown  into  one,  was  taken  out  for 
one  story  and  replaced  by  columns  about  16  ft.  apart. 
These  columns  were  supported  on  the  rubble  wall,  which, 
being  intended  only  to  carry  a  continuous  brick  wall,  was 
unfit  to  carry  the  concentrated  weight  of  the  columns. 
Spreading  beams  under  these  columns  would  doubtless  have 
saved  the  building. 

Suppose  in  Fig.  4  the  load  on  the  column  is  150,000  Ib. 
At  200  Ib.  per  sq.  in.  on  the  rubble  wall  a  flange  area  of  i 
beams  of  750  sq.  in.  would  be  required.  Assuming  I-beam 
flanges  4  in.  wide  a  length  of  188  in.  or  15  ft.  8  in.  is 
needed.  This  will  be  made  up  of  2  beams  7  ft.  10  in.  long. 
The  pressure  per  lineal  foot  is  200  X  4  X  12  =  9,600  Ib., 
and  the  span  of  the  cantilever  is  3  ft.  6  in.  The  bending 
moment  is  705,600  in.  Ib.  and  the  section  modulus  required 
at  16,000  Ib.  per  sq.  in.  is  705,600  ~  16,000  =  44.1.  The 
size  of  I-beam  required  is  then  a  12  in.  40  Ib.  beam.  As 
the  flange  width  is  more  than  4  in.,  a  revision  of  the  cal- 
culations could  be  made  using  the  5^4  in.  width  of  this 
beam  and  trying  again  for  the  bending  moment. 

Beams  and  rails  are  often  imbedded  in  concrete  footings 
and  pedestals  to  distribute  the  pressure  over  a  greater 
surface,  the  beams  being  used  to  give  the  resistance  to 
bending  which  the  concrete  lacks.  Rails  are  not  economical 
for  this  purpose,  unless  they  happen  to  be  old  rails  on  hand 
or  purchasable  at  a  much  lower  rate  per  Ib.  than  I-beams. 
For  the  same  weight  of  metal  much  greater  rigidity  can 
be  obtained  in  light  weight  I-beams  than  in  rails.  The 
concrete,  instead  of  being  counted  upon  to  assist  the  steel, 
34C 


o 

_ 


346 


is  merely  the  medium  to  transmit  the  upward  pressure  of 
the  soil  into  the  beams,  to  hold  them  against  buckling,  and 
to  protect  them  from  rust. 

In  Fig.  5  assume  a  load  of  600,000  Ib.  on  the  column 
shown.  Allowing  250  Ib.  per  sq.  in.  bearing  on  the  con- 
crete this  would  require  a  bearing  area  in  the  flanges  of 
the  I-beams  of  2,400  sq.  in.,  or,  assuming  the  flange  to  be 
6  in.  wide,  a  total  length  of  I-beam  of  400  in.  or  33  ft.  4  in. 
This  will  be  made  up  of  4  beams  8  ft.  4  in.  long.  The 
upward  pressure  on  the  beam  is  6X250=1,500  Ib.  per 
in.  or  18,000  Ib.  per  ft.  of  beam.  The  overhang  of  the 
cantilever  is  3  ft.  &/2  in.  and  the  maximum  moment  is 
18,000x3.542x3.542x^2x12=1,355,000  in.-lb.  Dividing  this 
by  16,000,  the  extreme  fiber  stress  allowed,  we  have  84.7 
as  the  section  modulus.  The  beams  will  therefore  be  18 
in.  I's  55  Ib.  per  ft.  (S  =  88.4). 

A  grillage  of  I-beams  crossing  at  right  angles  to  each 
other  as  indicated  in  Fig.  6  is  used  to  distribute  the  load 
of  a  column  over  a  rectangular  concrete  base.  In  calculat- 
ing the  bending  moment  on  the  beams  the  point  of  sup- 
port of  the  cantilever  should  not  be  taken  as  the  edge 
of  the  flange  of  the  beam  above  or  the  edge  of  the  column 
base,  but  as  some  point  where  a  good  substantial  support  is 
assured,  as  indicated  in  Fig.  6,  the  span  of  the  cantilever 
being  /. 

It  is  sometimes  necessary  to  place  a  column  pedestal  so 
as  not  to  project  beyond  the  property  line,  where  the  col- 
umn center  is  located  but  a  foot  or  so  within  the  property 
line.  No  form  of  footing  will  give  effective  bearing  on  the 
soil  for  a  width  more  than  three  times  the  distance  from 
the  outside  line  of  the  footing  to  the  center  of  the  column, 
unless  it  be  a  cantilever  balanced  by  interior  loads.  Can- 
tilevers are  sometimes  employed  which  are  supported  on  2 
pedestals  within  the  property  lines,  and  which  in  turn 
support  2  columns.  Figs.  7  and  8  illustrate  cantilever  sup- 
ports of  wall  columns  both  for  a  narrow  building,  where 
the  2  outside  columns  may  rest  on  the  same  set  of  can- 
tilever beams,  and  a  building  where  an  interior  column 
347 


348 


is  utilized  to  take  the  uplift  of  the  cantilever.  The  span 
of  the  cantilever  beams  is  the  distance  from  center  of  col- 
umn to  the  center  of  the  group  of  supporting  beams.  The 
depth  of  cantilever  beam  should  be  selected  with  the 
length  5"  in  view,  making  it  sufficient  to  prevent  too  great 
deflection  upward,  say  not  shallower  than  1-20  of  £.  The 
cantilever  may  be  composed  of  rolled  beams  or  of  a  box 
girder.  If  below  the  surface  of  the  ground  or  cellar  floor, 
the  steel  work  should  be  protected  by  concrete.  The  box 
girder  may  be  riveted  to  the  side  of  the  column  or  may 
have  interior  diaphragm  and  stiffeners  equivalent  in  area 
to  the  column,  with  the  column  resting  on  top.  The 
I-beams  should  have  separators  or  riveted  diaphragms  be- 
tween them. 

The  safe  carrying  power  of  masonry,  according  to  the 
New  York  Building  Code,  is  as  follows,  in  tons  per  sq. 
ft. :  Brick  in  lime  mortar,  8 ;  brick  in  lime  and  cement 
mortar,  11.5;  brick  in  cement  mortar,  15;  rubble  in 
Portland  cement  mortar,  10;  rubble  in  other  than  Port- 
land cement  mortar,  8;  rubble  in  lime  and  cement  mor- 
tar, 7;  rubble  in  lime  mortar,  5;  Portland  cement  con- 
crete, 15;  other  than  Portland  cement  concrete,  8. 

These  units  are  less  than  those  given  a  few  paragraphs 
preceding  for  columns,  etc.,  resting  on  masonry,  as  they 
should  be.  Those  are  for  a  load  on  only  a  portion  of  the 
top  of  a  wall  or  pier,  while  these  are  for  the  entire  wall 
or  pier. 

While  no  general  rule  prevails  for  the  load  on  high 
walls,  diminishing  the  unit  as  the  ratio  of  height  to  width 
increases,  it  is  true  that  high  walls  not  braced  should  not 
be  loaded  with  the  above  limiting  loads.  Some  such  rule 
as  this  would  be  a  safe  basis  upon  which  to  proportion 
walls  that  are  heavily  loaded,  namely ;  for  walls  whose 
height  is  10  times  the  thickness,  or  less,  use  the  units 
above  given,  and  for  walls  whose  height  is  25  times  the 
thickness,  use  2-3  of  the  same,  walls  between  10  and  25 
times  the  thickness  to  have  proportionate  units  between 

349 


these  limits.  Walls  more  than  25  times  their  thickness  in 
unsupported  height  are  to  be  avoided. 

For  an  upward  pull,  such  as  the  anchorage  of  a  can- 
tilever or  the  uplift  of  the  post  of  a  railroad  bent  due  to 
wind  load,  rods  or  bars  should  go  down  deep  enough 
into  the  masonry  to  take  a  weight  of  the  same  50  per  cent 
in  excess  of  the  calculated  uplift.  If  the  masonry  is  brick 
or  rubble,  there  should  be  a  grillage  of  beams  or  rails  so 
arranged  that  they  would  lift  the  necessary  weight  of 
masonry.  For  very  heavy  anchorages  in  concrete,  grillages 
should  also  be  provided.  For  a  small  uplift  in  concrete 
a  good  sized  washer  plate  is  usually  sufficient.  The  anchor 
bolts  should  have  a  square  head,  and  the  washer  plate 
should  have  a  small  stop  plate  riveted  on  it  to  keep  this 
head  from  turning.  Cast  washers  may  be  made  with  a 
recess  in  which  the  head  of  the  bolt  will  fit.  A  split  bolt 
and  wedge  should  not,  in  general,  be  depended  upon  for 
anchorage  against  an  uplift.  The  holding  power  of  such 
a  bolt  is  more  or  less  uncertain,  and  the  chances  are 
many  that  the  bolts  will  not  all  be  properly  set. 

These  split  bolts,  passing  into  the  masonry  a  foot  or 
two,  are  commonly  used  for  anchorage  of  stringers  and 
girders  and  trusses  of  bridges  where  no  uplift  is  counted 
upon. 

Columns  for  office  buildings  are  not  usually  anchored. 
The  cast  steel  or  cast  iron  bases  are  generally  left  untooled 
on  the  bottom,  and  holes  are  cored  in  the  bottom  plate 
through  which  grout  is  poured  after  the  base  is  leveled  up. 

No  anchor  bolts  of  any  kind  should  be  close  to  the 
edge  of  a  concrete  wall  or  pier,  as  the  driving  may  break 
out  the  concrete 

The  stability  of  a  masonry  pier  against  horiontal  or 
overturning  forces  is  met  largely  by  the  weight  of  the 
pier.  Figs.  2  and  3  illustrate  piers  subject  to  such  forces, 
and  the  remarks  made  in  regard  to  these  figures  relate 
to  provision  for  their  stability,  treating  the  vertical  pres- 
sure on  the  soil  only.  In  addition,  if  the  forces  are  hori- 
zontal or  have  horizontal  components,  there  is  provision 
350 


against  sliding  to  be  considered.  If  we  assume  a  coeffi- 
cient of  friction  of  the  pier  on  the  soil  as  ^,  we  should 
have  a  horizontal  projection  l/2  of  the  vertical  projection 
in  the  line  of  the  resultant  pressure.  Any  earth  packed 
against  the  side  of  the  pier  will  be  an  additional  safe- 
guard against  sliding.  It  is  best  in  the  case  of  a  constantly 
exerted  force  not  to  depend  upon  earth  exerting  horizontal 
pressure  against  a  vertical  surface,  as  the  force  will  tend 
to  compact  the  earth  and  move  the  pier. 

In  the  case  of  a  pier  for  a  mill  building  column  or  a 
crane  runway  column  the  horizontal  forces  due  to  the 
wind  against  the  building  or  due  to  the  thrust  of  the  crane 
are  only  occasionally  exerted  and  very  seldom  to  their 
full  extent.  It  is  safe  in  such  cases  to  allow  for  some 
horizontal  pressure  exerted  by  the  earth. 

To  arrive  at  a  means  of  finding  approximately  the  sta- 
bility imparted  by  the  lateral  pressure  of  the  earth,  take 
the  case  shown  in  Fig.  9.  This  represents  a  pole  placed 
in  the  ground  and  subject  to  a  lateral  force.  The  weight 
here  is  negligible  If  we  assume  that  the  pole  turns  about 
a  point  2-3  of  the  depth  below  the  ground,  the  resistance 
of  the  earth  will  vary  uniformly  from  this  point  down, 
and  would  vary  uniformly  from  the  same  point  up,  but 
for  the  fact  that  this  would  make  the  maximum  pressure 
occurring  at  the  ground  level.  Because  the  lateral  pres- 
sure in  ordinary  earth  at  the  ground  surface  would  be 
practically  nil,  it  is  taken  as  varying  from  zero  at  the 
ground  to  a  maximum  somewhere  below  the  surface.  This 
is  arbitrarily  taken  at  1-3  of  the  depth  from  the  surface. 
It  is  safe  to  say  that  well  compacted  soil  will  stand  a 
lateral  force,  for  a  short  time,  a  few  feet  below  the  sur- 
face, of  500  Ib.  per  sq.  ft.  and  about  twice  this  amount 
at  a  depth  of  5  or  6  ft.  below  the  surface,  all  without  ap- 
preciable settlement.  Now  if  P  be  assumed  as  constant,  Q 
will  depend  in  amount  upon  Ft  as  it  must  be  the  differ- 
ence between  P  and  F.  For  a  small  force  at  F  and  a  long 
lever  arm  L,  Q  will  approach  equality  with  P.  Hence  the 
351 


approximate  moment  of  stability  in  ft.-lb.  about  a  section 
at  the  force  P  will  be 


Thus  a  pole  i  ft.  in  diameter,  30  ft.  above  the  ground 
and  6  ft.  in  the  ground  would  stand  3,350  ft.-lb.  or  a  force 
of  105  Ib.  horizontally  at  the  top.  If  the  ground  is  hard 
and  rocky  or  if  there  is  a  pavement  around  the  pole,  it 
will  stand  much  more  than  this. 

The  moment  of  stability  of  a  column  and  pier  due  to 
their  weight  is  equal  to  the  product  of  the  total  weight 
(under  the  condition  of  maximum  horizontal  pressure) 
and  1-6  of  the  base. 

To  take  an  example,  suppose  a  column  supporting  a 
crane  runway  is  anchored  to  a  pier  6  ft.  deep  and  5  ft. 
by  4  ft.  in  plan.  The  pier  on  account  of  its  being  planted 
in  the  ground  will  have  a  moment  of  stability  2  ft.  below 
the  ground  line  of  92  X  36  X  4  =  13,250  ft.-lb.  On  ac- 
count of  its  weight  (taking  the  weight  of  the  pier  as  18,000 
Ib.  and  the  minimum  load  on  the  column  under  the  condi- 
tion considered  as  10,000  Ib)  a  moment  of  stability  of 
28,000X1=28,000  ft.-lb.  at  the  base  of  pier.  At  a  height 
of  20  ft.  above  the  ground  the  former  moment  would  al- 
low a  force  of  13,250  -r-  22  =  602  Ib.  and  the  latter  would 
allow  28,000-^-26=1,080  Ib.  A  total  thrust  of  1,682  Ib. 
could  be  exerted  at  this  height.  In  general  2  columns  of 
a  runway  will  be  acted  upon  by  the  sudden  stopping  of  a 
load  carried  by  the  crane.  The  coefficient  of  sliding  friction 
is  usually  taken  as  1-5.  The  load  on  the  trolley  could 
then  be  2  X  5  X  1,682  =  16,820  Ib.  This  pier  would  then 
do  for  about  an  8  ton  crane  runway.  In  a  similar  manner 
the  stability  of  a  mill  building  column  against  wind  loads 
may  be  worked  out.  No  rigid  analysis  has  been  attempted 
of  the  forces  in  Fig.  9,  but  simply  a  rough  approximation 
of  the  stability  imparted  to  a  post  or  pier  planted  in  earth 
which  is  tamped  around  it. 

The  allowed  slope  on  a  concrete  footing,  such  as  either 
the  two  forms  shown  in  Fig.  10,  may  be  investigated 
352 


- 


as  follows:    The  bending  moment  under  the  edge  of  wall, 
at  £  tons  per  sq.  ft.  upward  pressure  of  soil  is 


The  resisting  moment,  at  40  Ib.  per  sq.  in.  safe  modulus 
of  transverse  strength  is  40  h2  ~  6,  both  on  a  rectangle  h 
in.  deep  and  I  in.  wide.  Equating  these  we  find  the  fol- 
lowing to  be  very  nearly  true: 

Sp*  =  h* 

Thus  for  a  pressure  on  the  soil  of  2  tons  per  ft.  the 
depth  of  the  footings  should  be  1.4  times  the  projection 
beyond  the  wall.  For  a  4  ton  earth  pressure  the  depth 
should  be  2  times  the  projection. 

In  a  brick  footing  no  reliance  can  be  placed  upon  tensile 
strength  of  the  mortar  in  the  vertical  joints,  but  inde- 
pendent of  this  there  is  a  tensile  strength  in  a  brick  wall 
derived  from  the  bonding  of  the  bricks.  The  friction  of 
each  brick  against  the  upper  and  lower  adjacent  tiers  re- 
sists the  tendency  to  draw  it  out  of  place.  Assume  the 
coefficient  of  friction  to  be  l/2.  If  the  earth  pressure  at 
the  base  of  the  footing  is  I  ton  per  sq.  ft.  there  will  be 
1-9  of  this  pressure  on  the  top  and  on  the  bottom  of  the 
half  of  a  brick.  Hence  1-9  of  2,000  Ib.  will  be  required 
to  pull  out  a  brick.  This  on  16  sq.  in.  (the  section  of  a 
brick  longitudinally)  is  14  Ib.  per  sq.  in.  Allowing  a  factor 
of  safety  of  5  to  cover  irregular  bonding  we  have  an  al- 
lowed tension  of  3  Ib.  per  sq.  in.  Using  these  values  as 
above  for  the  concrete  footing  we  find 

h  =  373  p. 

Since  the  allowed  tension  on  the  brick  footing  is  directly 
proportional  to  the  earth  pressure,  this  relation  will  hold 
true  for  any  other  earth  pressure.  It  requires  good  bond- 
ing of  brick  work  to  distribute  the  load  on  a  spread  founda- 
tion, even  with  the  small  spread  that  this  formula  would 
give. 

From  the  standpoint  of  the  allowed  shear  on  the  con- 
crete, using  Fig.  10,  the  amount  of  pressure  on  the  projec- 
tion for  an  earth  pressure  of  I  ton  per  sq.  ft.  is  2,000  />. 
353 


11 

VI&  OJ  .iVlCJ 


•:'«'4 

&;•: 


v:$ 


"•;<< 


.'.^:-; 


354 


The  area  in  shear  is  144  h  sq.  in.     Allowing  40  Ib.  per  sq. 
in.  we  have  5,760  h  =  2,000  p,  or 
h  =  .35  p. 

Sometimes  the  upward  pressure  of  the  soil  is  resisted 
by  needle  beams  under  a  wall,  of  old  rails  or  I-beams. 
In  Fig.  ii  assume  the  upward  pressure  of  the  soil  as  2 
tons  per  sq.  ft.  and  the  imbedded  beams  spaced  il/2  ft. 
apart.  This  upward  pressure  will  be  the  same  as  a  vertical 
downward  load  on  the  beams,  which  will  be  cantilevers 
having  an  overhanging  of  3  ft.  The  middle  distance  of  I 
ft.  6  in.  is  taken  less  than  the  width  of  the  wall,  as  some 
space  is  required  for  bearing.  The  bending  moment  on 
each  beam  is  il/2  X  4>oooX  3  X  ll/2  =  27,000  ft.-lb.  or 
324,000  in.-lb.  The  value  of  the  section  modulus  required 
is  324,000  -f-  16,000  =  20.25.  The  section  modulus  of  a  10 
in.  I-beam  25  Ib.  is  24.4,  hence  this  size  of  beam  would  be 
used.  It  would  take  4  55  Ib.  rails  or  73.3  Ib.  per  ft.  to  give 
the  same  stiffness. 

Reinforced  concrete  slabs  are  now  much  used  in  place 
of  the  needle  beams  shown  in  Fig.  n.  Fig.  12  shows  a 
slab  of  the  kind  referred  to.  We  have  seen  that  in  order 
to  have  a  proper  shearing  area  we  should  have  for  every 
ton  of  earth  pressure  a  depth  h  equal  to  .35  p,  or  if  S  be 
the  pressure  of  the  soil  in  tons  per  sq.  ft., 

h  =  -3SP$  (i) 

If  we  use  square  rods  for  the  reinforcement,  and  place 
them  as  indicated  in  the  figure,  we  should  have  the  rod  im- 
bedded for  50  diameters,  or  p  =  500?.  Allowing  12,500  Ib. 
per  sq.  in.  on  the  steel,  and  remembering  that  the  amount 
of  stress  in  the  concrete  must  be  the  same  as  that  on  the 
steel,  we  have  for  a  section  x  in.  wide  and  h  in.  deep. 

M=12SWd2X~  =8S54</2>* 

Substituting  for  h  its  value,  .35  pS,  we  have  M  =  3099  p 
d*S  in.-lb.  From  the  soil  pressure  of  6*  tons  per  sq.  ft. 
we  have 


355 


Equating  these  two  values  of  M  and  using  for  P  its 
value  Sod  we  have 

x  =  8.93  d,  or,  say,  9  d. 

It  is  thus  seen  that  for  any  upward  pressure  the  same 
rods  would  be  used  in  a  given  projection  p.  These  rods 
would  have  a  diameter  1-50  of  this  projection  and  be  spaced 
9  times  their  diameter  apart.  For  different  earth  pressures 
the  height  h  would  vary  as  per  equation  (i). 

The  foregoing  does  not  take  account  of  the  stress  on 
the  concrete,  but  it  will  be  found  by  trial  that  the  depth 
of  slab  required  for  any  earth  pressure  above  about  l/t  ton 
per  sq.  ft.  would  give  concrete  enough  to  keep  the  stress 
on  the  same  within  safe  limits. 

In  a  square  slab  supporting  a  column  similar  reinforce- 
ment can  be  used.  The  slab  should  be  surmounted  by  a 
plinth  or  block  of  concrete  upon  which  the  column  rests. 
The  depth  of  the  slab  should  be  governed  by  the  upward 
pressure  of  the  soil  on  all  of  the  area  of  slab  outside  of 
this  plinth,  allowing  a  unit  in  shear  (on  the  section  that 
would  be  sheared  if  this  plinth  should  sink  into  the  soil) 
of  40  Ib.  per  sq.  in.  Rods  should  all  pass  under  this  plinth ; 
that  is,  there  should  be  4  sets,  2  parallel  to  the  sides  of  the 
slab  and  2  diagonally.  Rods  parallel  to  the  sides  of  the 
slab  lying  toward  the  edges  and  not  under  the  plinth 
would  be  of  little  or  no  use.  They  will  only  serve  to  in- 
tensify the  stress  on  the  rods  at  right  angles  to  themselves 
that  do  lie  under  the  upper  block  or  plinth.  The  use  of 
rods  at  right  angles  to  each  other  spaced  uniformly  both 
ways  is  a  common  but  irrational  method  of  reinforcement. 


Shear  of  Concrete  and  Its  Bearings  on 
the  Design  of  Beams. 

The  unit  shearing  strength  of  concrete  is  between  i  and 
2  times  its  unit  tensile  strength  for  practical  purposes  in 
1  the  design  of  beams. 

In  making  this  assertion  the  writer  appreciates  the  fact 
that  it  is  a  broad  statement.     He  realizes  that  it  is  an  as- 
356 


sertion  that  will  be  contradicted.  It  is  not  for  the  mere 
purpose  of  raising  a  controversy  that  this  seeming  dogma 
is  put  at  the  head  of  this  article.  If  the  statement  is  right, 
it  should  be  given  a  very  prominent  place  in  every  work  on 
the  subject  of  reinforced  or  plain  concrete  design.  If  it  is 
wrong,  it  is  the  duty  of  anyone  who  can  show  it  to  be 
wrong  to  give  a  sound  reason  therefor. 

Recently  some  tests  on  the  shearing  strength  of  concrete 
were  made  at  the  Engineering  Experiment  Station  of  the 
University  of  Illinois,  under  the  direction  of  Professor 
Arthur  N.  Talbot.  These  tests  have  been  given  a  wide 
publicity.  Rightly  interpreted  they  are  very  valuable. 
Wrongly  interpreted  they  may  lead  to  another  crop  of  dis- 
astrous failures  in  reinforced  concrete  construction.  The 
tests  referred  to  appear  to  show  that  concrete  has  a  shear- 
ing strength  nearly  equal  to,  and  in  some  cases  in  excess  of, 
the  compressive  strength  per  sq.  in.  In  other  words,  they 
lead  to  the  conclusion  that  the  strength  of  concrete  in 
simple  shear  is  8  or  10  times  its  strength  in  tension. 

In  making  these  tests  special  efforts  were  made  to  elim- 
inate every  other  stress  except  simple  shear.  In  the  writ- 
er's opinion  the  very  means  empfoyed  introduced  elements 
that  to  a  large  extent  diminish  the  value  of  the  tests  as 
helps  in  design  Reference  will  be  made  to  these  features 
of  the  tests  later.  Professor  Talbot  states  that  the  tests 
are  open  to  objection.  It  is  the  objectionable  features 
that  the  writer  wishes  to  emphasize. 

It  is  not  questioned  that  the  results  of  the  tests  give 
close  to  the  true  value  of  shear  in  concrete  in  the  strait- 
ened conditions  in  which  the  concrete  of  the  tests  was 
placed.  An  attempt  will  be  made,  however,  to  show  that  the 
"laboratory"  feature  of  the  tests  was  so  intensified  by 
eliminating  the  beam  action,  that  the  results  are  apt  to  be 
very  misleading  if  applied  to  design.  The  unit  stress  al- 
lowed in  shear  on  concrete  by  various  building  codes  is  in 
the  neighborhood  of  40  or  50  Ib.  per  sq.  in.  Now  if  the 
material  has  a  shearing  strength  of  1,000  to  2,000  Ib.  per 
sq.  in.,  it  is  a  waste  of  material  and  an  economic  blunder 

357 


to  allow  only  50  Ib.  in  design.  It  would  not  be  surprising 
if  a  class  of  designers  should  rise  up  and  call  for  a  raising 
of  this  low  unit  to  a  fair  factor  of  safety  based  on  the 
high  units  determined  by  these  tests,  especially  in  view  of 
the  high  authority  from  which  they  emanate.  It  would 
further,  not  be  surprising  if  the  work  turned  out  by  these 
same  designers  should  lead  to  added  work  for  coroners. 

One  feature  of  this  discussion  concerns  the  difference  in 
the  shearing  strength  of  concrete :  ( i )  when  in  tension 
at  right  angles  with  the  plane  of  shear;  (2)  when  under 
no  stress  whatever  at  right  angles  with  the  plane  of 
shear,  but  free  to  move  in  that  direction;  (3)  when  un- 
der no  stress  at  right  angles  with  the  plane  of  shear,  but 
confined  so  that  any  motion  would  induce  such  stress;  (4) 
when  under  compression  at  right  angles  with  the  plane  of 
shear. 

It  is  plain  that  under  condition  (i)  failure  would  occur 
the  most  readily,  and  under  condition  (4)  it  would  be  least 
liable  to  occur.  In  fact  there  would  be  a  large  apparent 
shearing  strength  between  2  concrete  surfaces  completely 
severed,  if  these  surfaces  were  forced  together  by  a  com- 
pressive  stress,  due  to  the  mere  friction  of  the  surfaces. 
This  element  would  be  completely  lacking  in  (i),  and  a 
small  tensile  stress,  coupled  with  a  shearing  action,  would 
cause  failure. 

Now  the  conditions  in  the  tests  referred  to  agree  closely 
with  (3)  and  approach  (4),  while  the  conditions  in  actual 
beams  in  a  building  agree  nominally  with  (2)  but  approach 
(i).  This  latter  is  due  to  the  tendency  of  a  slab  to  shrink 
between  beams  and  of  a  beam  to  shrink  between  columns, 
giving  an  initial  tension  throughout  the  beam  or  slab.  One 
set  of  tests  was  made  by  punching  out  a  cylindrical  piece 
from  a  concrete  plate  or  slab.  Now  if  this  cylindrical 
piece  had  been  a  separate  piece  cast  in  a  hole  in  the  plate, 
with  no  bond  whatever,  but  merely  fitting  snugly  in  the 
hole,  it  would  take  much  force  to  push  it  out.  The  appar- 
ent but  false  shearing  strength  would  be  very  considerable. 
This  would  come  under  the  head  of  condition  (3),  above, 

358 


but  the  actual  shearing  strength  would  be  zero.  Molded 
in  one  piece  a  concrete  plate  would  then  have  an  apparent 
shearing  strength  which  would  be  the  sum  of  what  actual 
shearing  strength  the  concrete  possesses  and  this  false 
shearing  strength  that  might  be  said  to  be  due  to  the 
crowding  of  the  material.  This  would  be  true  in- 
dependent of  shrinking  in  the  concrete.  As  an  illus- 
tration of  the  effect  of  the  crowding  of  the  material,  it 
requires  more  force  to  punch  a  hole  in  a  steel  plate  when 
the  clearance  between  the  die  and  punch  is  small  than 
when  it  is  larger,  this  in  spite  of  the  fact  that  steel  is 
stronger  in  tension  than  in  shear. 

Shrinking  of  the  concrete  block  from  which  the  piece 
is  punched  adds  a  new  element  of  apparent  shearing 
strength  in  that  it  grips  the  "punching"  and  adds,  to  the  2 
other  elements  that  go  to  make  up  the  force  necessary 
to  push  it  out,  that  of  friction  on  its  sides.  That  more 
load  was  required  to  force  out  a  punching  in  a  block  that 
was  reinforced  with  straight  rods  arranged  in  a  square 
around  the  tested  portion,  and  still  more  when  hoops  were 
used,  is  strong  evidence  of  the  effect  of  crowding  of  the 
material  or  of  the  compression  that  will  be  induced  normal 
to  the  shearing  surface  by  the  mere  action  of  the  material 
under  the  shearing  test.  It  takes  a  strong  pull,  sometimes, 
to  draw  the  cork  out  of  a  bottle.  There  is  no  element  of 
shear  in  it,  but  if  this  friction  were  combined  with  a  small 
shearing  strength,  the  sum  would  be  an  apparent  shearing 
strength  of  no  small  value. 

In  another  set  of  tests  constrained  beams  were  used. 
These  beams  were  so  short  that  but  little  in  the  way  of 
beam  stresses  could  be  expected,  especially  because  the 
edge  of  the  load  and  the  edge  of  the  support  were  almost 
vertically  over  each  other.  But  the  induced  stresses  of 
(3)  would  be  very  clearly  a  possibility  in  these  tests.  The 
crowding  of  the  material  would  add  a  false  element  to  the 
apparent  shearing  strength  which  would  be  of  unknown 
value. 

The  features  of  these  tests  that  render  the  application 


of  their  results  to  design  not  only  questionable  but  dan- 
gerous are  these:  (a)  The  test  speciments  do  not  resem- 
ble anything  in  which  concrete  is  used  practically,  (b) 
The  loads  applied  on  the  specimens,  instead  of  being  flexi- 
ble and  taking  the  shape  of  the  deflecting  part,  were  in 
themselves  rigid  for  the  entire  extent  of  their  bearing  on 
the  concrete,  (c)  There  is  scarcely  any  case  in  practice 
where  shear,  pure  and  simple,  is  exerted  on  any  part  of  a 
structure  in  concrete.  This  last  is  emphasized  in  the  futile 
attempts  to  manufacture  a  condition  where  simple  shear 
occurs.  In  view  of  the  fact  that  simple  shearing  action  is 
not  a  structural  possibility,  it  is  not  clear  why  strenuous 
attempts  should  be  made  to  approach  it  in  test  specimens. 
Concrete  is  unlike  steel  in  that  it  is  5  or  10  times  as 
strong  in  compression  as  it  is  in  tension,  whereas  structural 
steel  is  about  equally  strong  in  either.  Steel  is  little  af- 
fected in  its  shearing  strength  by  the  simultaneous  occur- 
rence of  tension  or  compression.  The  principles  of  design 
employed  in  steel  beams  and  girders  must  therefore  be 
modified  before  they  can  be  applied  to  the  design  of  rein- 
forced concrete  beams. 

Concrete  is  further  quite  different  from  wood,  in  that 

i    the  latter,  while  it  possesses  great  tensile  strength  in  the 

direction  of  the  grain,  and  large  compressive  strength  in 

i    the  opposite  direction,  has  very  little  tensile   strength  at 

1    right  angles  to  the  grain.    The  shearing  strength  of  wood 

5    in  a  direction  parallel  to  the  grain  is  small,  because  of  the 

little  tensile  strength  normal  to  the  grain.     If  wood  were 

I    tightly    held    together    with    tension    bands,    its    apparent 

j    shearing  strength  parallel  to  the  grain  would  be  largely 

e    increased. 

•t ;      About  the  only  common   structural  material  that  con- 

il    crete  resembles  is  cast  iron.     The  tensile  strength  of  the 

ie    latter  in  all  directions  is  only  a  fraction  of  its  compressive 

ic    strength.     The   practical   value   of  cast   iron   in   shear   is 

n    comparatively   small   because   of   its   weakness   in   tension. 

and  yet,  no  doubt,  in  a  restrained  beam  of  short  span  a 

block   of  cast   iron   would   resist  a  high   shearing:  strain, 

360 


The  term  "practical  shearing  strength"  is  here  used  not  only 
to  distinguish  from  the  theoretical  but  also  from  ideal. 

It  is  next  to  impossible  to  eliminate  tensile  stresses  in 
concrete  beams  and  slabs,  and  shear  failures  will  be  ac- 
companied in  general  by  tension  failures.  They  will  be 
so  closely  associated  together  that  it  will  scarcely  be  pos- 
sible to  separate  them.  In  fact  shear  and  tension  must 
be  considered  as  generally  acting  together  in  beams.  A 
practical  working  unit  stress  for  shear  in  beams  should 
take  into  account  the  ever  present  tension.  Building  ordi- 
nances rightly  prescribe  low  units  for  shear.  Reinforcement 
of  beams  against  shearing  stresses,  as  very  often  practiced, 
is  not  rational. 

In  Fig.  i  we  have  a  simple  beam  uniformly  loaded.  The 
load  in  this  case  is  of  course  flexible  and  will  take  the 
shape  of  the  deflected  beam  The  shear  increases  from 
the  center  of  beam  to  the  support.  Herein  is  this  beann 
essentially  different  from  a  test  beam  in  which  the  load: 
is  a  rigid  block  the  length  of  the  beam  and  in  which  the 
shear  is  all  confined  in  a  narrow  space  between  the  edge 
of  the  block  and  the  edge  of  the  support.  The  beam  in 
Fig.  I  represents  actual  conditions. 

The  load  between  B  and  F  can  be  assumed  as  carried 
on  the  surfaces  AB  and  FG.  CD  represents  l/2  of  this  load. 
This  may  be  resolved  into  CE  and  ED.  ED  is  the  shear 
along  the  surface  AB.  CE  is  tension  on  the  same  surface. 
The  critical  point  in  the  strength  of  this  beam  is  the  ten- 
sion on  the  surface  AB.  If  this  tension  becomes  too  great1 
on  this  section  the  beam  will  fail.  It  is,  of  course,  a  ten- 
sion failure,  but  in  practice  it  is  interpreted  as  a  failure 
in  shear.  In  considering  the  design  of  a  beam  it  is  held  to 
be  weak  in  shear  in  a  section  near  the  ends,  because  of' 
the  known  tendency  of  beams  to  fail  in  a  line  approxi- 
mating AB. 

In  order  to  find  the  value  of  the  angle  X  to  give  the 
tension  on  A  B  a  maximum,  assume  a  depth  of  beam  i-id 
of  the  clear  opening,  as  shown  in  Fig.  I.    Assume  also  a 
361 


/.one/    w  pe 


FIG.   1.     SIMPLE   BEAM   UNIFORMLY 
LOADED. 


FIG.    2.     COMPOSITE   SKETCH   SHOWING 
CRACKS  IN  BEAMS. 


3 


K 
. 


.-J-g  ---  ---  .  -l.  —  1_  j._  i 


*.^ 


(dj 


FIG.   3.      SHOWING   SEVERAL   METHODS 
OF  REINFORCING  BEAM  FOR  SHEAR.. 


(a) 


m 


\ 


i 


(b) 

FIG.    4.      SHOWING    SOCALLED   HOWE   & 
PRATT   TRUSSES. 


width  of  beam  of  I  ft.  From  the  trigonometric  relations 
we  find 

C  E  =  C  D  cos  X. 

But  C  D  —  wL  (l/2  —  i-io  cot  X). 

Hence  C  E  =  (y2— i-io  cot  X)  wL  cos  X. 

If  we  divide  this  value  of  C  E  by  the  length  A  B  (equal 
area  of  section  in  tension),  we  have 

Unit  tension  on  A  B  =  (5  sin  x  cos  x  —  cos8  x)  w. 

Taking  the  differential  coefficient  of  this  expression  for 
the  unit  tension  and  equating  the  zero  we  obtain,  after  re- 
ducing 

5  cos  2  x  =  —  sin  2  x. 

From  which  we  have 

x  =  50  deg.  40  min. 

This  is  the  angle  which  gives  a  maximum  tension  on 
the  section  A  B.  From  this  we  have  a  unit  tension  of 
2.05  w. 

The  end  shear  worked  out  in  the  ordinary  way,  is  5  w. 
Thus  in  this  case  the  unit  strength  of  the  beam  in  simple 
shear  is  for  practical  purposes  2^2  times  its  tensile  strength. 
It  would,  in  fact,  be  less  than  this,  because  the  shear  D  E 
in  Fig.  i  is  acting  at  the  same  time,  and  shear  acting  in 
conjunction  with  tension  will  lessen  the  tensile  value. 

Using  Merriman's  formula  for  combined  shear  and  ten- 
sion, in  which  the  resultant  unit  tension  equals  l/2  of 
the  direct  unit  tension  plus  the  square  root  of  the  sum 
of  the  square  of  the  unit  shear  and  ^  of  the  square 
of  the  direct  unit  tension,  we  find  for  this  case  a  result- 
ant unit  tension  of  3.73  w.  Comparing  this  with  the 
unit  shear  found  in  the  ordinary  way  (the  reaction  of 
beam  -f-  area  of  vertical  section,  or  5  w),  we  find  that  the 
unit  strength  is  for  practical  purposes  I  1-3  times  the  ten- 
sile strength. 

If,  instead  of  making  the  depth  i-io  of  the  span,  it  be 
made  1-20  of  the  span,  we  find  after  a  process  similar  to  the 
above,  10  cos  2  x  —  —  sin  2  x,  or  x  =  47  deg.  51  min. 
The  unit  tension  is  found  to  be  4.53  w.  The  unit  shear, 
found  in  the  ordinary  way,  is  10  w.  Hence  the  unit  shear- 


ing  strength  is,  for  practical  purposes,  about  2l/±  times  the 
unit  tensile  strength,  or  about  i%  times,  when  reduced  for 
combined  shear  and  tension.  Most  beams  will  be  found 
to  be  between  i-io  and  1-20  of  the  span  in  depth.  It  would 
be  found  that  in  beams  less  than  1-20  of  the  span  in  depth 
this  apparent  shearing  strength  approaches  closer  to  the 
tensile  strength,  but  it  is  in  deep  beams  where  the  shear- 
ing strength  plays  the  most  important  part.  As  pointed 
out  in  an  article  in  this  journal,  published  Jan.  15,  1907, 
the  critical  depth  of  beam  from  the  standpoint  of  shear  is 
i-io  of  the  span  and  over.  The  capacity  of  a  shallow  beam 
in  bending  is  not  sufficient  for  it  to  carry  load  enough  to 
tax  its  capacity  in  shear. 

Other  forces  are  of  course  at  work  in  the  beam,  and 
these  may  tend  to  alter  the  line  of  failure,  so  that  it  would 
not  coincide  with  A  B  in  the  figure.  Tension  in  the  lower 
part  of  the  beam  begins  to  make  itself  felt  a  little  away 
from  the  support.  In  beams  where  the  bottom  reinforcing 
rods  stop  at  the  support,  and  therefore  lack  anchorage,  the 
combination  of  this  flange  tension  and  the  diagonal  tension 
may  reach  a  maximum  a  short  distance  from  the  support. 
If  a  beam  is  continuous  or  restrained  at  the  support,  there 
will  be  compression  at  the  bottom  of  beam  near  the  sup- 
port, and  this  too  will  tend  to  make  the  line  of  failure  or 
weakness  some  distance  away  from  the  support. 

Fig.  2  is  a  composite  sketch  showing  the  cracks  in  a  set 
of  10  beams  tested  by  the  writer.  The  diagonal  cracks  are 
very  plainly  characteristic  and  show  clearly  the  weakness 
of  reinforced  concrete  beams  in  this  respect.  These  beams 
were  reinforced  with  straight  horizontal  rods  near  the 
bottom  and  with  rods  across  the  support  to  take  the  con- 
tinuous action.  They  were  also  reinforced  with  so-called 
shear  bars,  that  is,  small  vertical  bars  or  rods  strung  along 
the  reinforcing  rods 

In  "Proceedings  of  the  American  Society  for  Testing 
Materials,"  Vol.  IV,  p.  498,  Prof.  F.  E.  Turneaure  de- 
scribes some  test  beams  which  were  6x6  in.  and  60  in.  in 
span,  reinforced  with  stirrups,  spaced  3  in.  apart.  On 
364 


page  507  Prof.  Turneaure  says:  "In  but  a  few  cases  was 
the  failure  free  from  the  influence  of  shearing  stresses,  but 
the  rupture  usually  occurring  outside  of  the  load  and  on 
a  diagonal  line."  The  stirrups  referred  to  are  supposed 
to  reinforce  the  beam  for  shear.  As  will  be  noted,  these 
test  beams  were  of  a  depth  i-io  of  the  span.  They  were 
therefore  of  a  depth  where  shearing  stresses  begin  to  play 
an  important  part. 

Another  characteristic  in  the  behavior  of  the  beams  rep- 
resented in  Fig.  2  is  the  horizontal  crack  just  above  the 
reinforcing  rod  These  beams  were  too  narrow  and  were 
consequently  lacking  in  shearing  strength,  in  a  plane  just 
above  the  rods,  to  take  the  horizontal  shear  or  the  grip- 
ping force  of  the  rods.  This  corresponds  to  horizontal 
shear  in  the  web  of  a  girder,  the  stress  that  the  flange  rivets 
must  convey  from  web  to  flange.  The  beams  of  which  this 
sketch  is  a  composite  were  designed  as  T-beams,  including 
in  their  calculation  the  floor  slab.  Thus  the  lower  part  of 
the  beam  did  not  have  enough  concrete  to  take  care  of  the 
stresses  in  the  steel.  When  it  is  considered  that  the  load 
upon  the  beams  was  only  that  which  the  designer  intended 
should  be  the  safe  carrying  capacity,  the  T-beam  is  seen 
to  be  weak  on  account  of  a  narrow  stem  that  does  not 
contain  enough  concrete  to  take  the  horizontal  shear  above 
the  rods.  Some  of  these  beams,  under  the  test  load,  showed 
only  vertical  cracks  starting  at  the  bottom  of  the  beam  and 
taking  in  the  reinforcing  rod.  One  beam  had  16  of  these 
cracks  in  its  length,  another  evidence  of  the  weakness  of  a 
T-beam. 

The  shearing  stress  just  above  a  horizontal  rod  in  a 
reinforced  concrete  beam  does  not  have  the  assistance  of 
any  initial  compression  to  relieve  the  effect  on  the  concrete. 
There  is,  further,  not  any  crowding  of  the  material  to  make 
failure  less  liable.  Reinforcement  with  short  diagonal  or 
vertical  rods  either  attached  to  the  horizontal  rods  or 
looped  over  them,  could  only  take  this  shear  by  localizing 
or  concentrating  the  stress  at  these  rods  and  introducing  a 
new  element  of  weakness. 

365 


It  is  a  remarkable  fact  that  if  we  apply  Merriman's  for- 
mula for  combined  shear  and  tension  and  make  the  tension 
zero,  we  find  that  the  tensile  unit  stress  due  to  shear  alone 
is  equal  to  the  shearing  unit  stress.  It  would  follow,  then, 
that  in  the  case  of  horizontal  shear  above  reinforcing  rods 
the  shearing  strength  is  equal  to  the  tensile  strength  of  con- 
crete. In  the  light  of  this  fact  a  T-beam  having  horizontal 
rods,  with  its  narrow  stem  and  large  percentage  of  steel, 
is  a  most  absurd  and  inefficient,  as  well  as  unscientific, 
form  of  construction. 

Fig.  3  shows  several  ways  of  reinforceing  a  beam  for 
shear.  That  shown  at  (a)  is  faulty  on  account  of  the  sharp 
bend  in  the  reinforcing  rod  (the  one  bent  up  toward  the 
support).  Failure  could  occur  on  the  diagonal  line  by 
simply  pulling  a  short  length  of  rod  out  of  the  concrete. 
At  (b)  and  (c)  failure  could  occur  by  the  pulling  out  of  a 
short  end  of  one  of  the  "shear  rods."  Explanation  of  how 
these  shear  rods  act  to  reinforce  a  beam  in  shear  seems  to 
be  lacking  in  technical  literature.  A  rod,  to  be  effective 
in  taking  stress,  must  either  be  anchored  at  the  end  by 
a  nut  and  washer,  or  some  equally  effective  means,  or  must 
be  buried  in  concrete  for  some  distance  beyond  its  point 
of  usefulness.  It  is  conceded  that  a  mesh  of  overlapping 
rods  will  be  some  aid  in  resisting  shearing  stresses.  As  an 
economic  proposition,  however,  this  means  of  reinforce- 
ment is  a  failure. 

A  steel  rod  in  shear,  that  is,  shear  in  the  steel,  stress  at 
right  angles  to  the  axis  of  the  rod,  is  an  absurdity.  Con- 
crete would  not  stand  the  side  force  of  a  rod  against  it 
that  is  stressed  in  shear  to  anything  like  a  reasonable  safe 
value  in  the  steel. 

In  Bulletin  No.  12  of  the  Illinois  Engineering  Experiment 
Station  the  results  of  some  tests  on  T-beams  are  given, 
which  illustrate  shear  reinforcement  with  vertical  rods.  In 
the  beams  the  tests  of  which  are  there  described  all  of  the 
portion  of  the  beam  in  shear,  namely,  the  end  third  at  each 
end,  is  reinforced  with  T/2  in.  U  bars  6  in.  apart.  There  is 
about  2po  in,  of  l/2  in.  corrugated  bars  in  the  stirrups  alone 
366 


in  a  beam  of  10  ft.  span.  This  steel  would  weigh  14  Ib.  If 
the  4  34-in.  plain  round  rods  found  in  one  beam  were  curved 
up  and  run  through  a  washer  plate  at  ends  of  span,  2  nuts 
on  each  end  of  each  rod  and  2  washer  plates  5-16  in.  thick 
and  7  in.  by  5  in.  would  not  weigh  as  much  as  these  stir- 
rups. Further,  these  parts  would  not  be  of  special  steel. 
Such  a  detail  would  give  a  positive  and  scientific  provision 
against  shear.  In  a  line  of  continuous  beams  rods  curved 
up  add  scarcely  any  length  or  cost.  Commenting  on  these 
tests  it  is  significant  to  note  that  the  unit  shears  given  by 
Professor  Talbot  as  existing  at  first  diagonal  crack  run 
from  180  Ib.  to  302  Ib.  per  sq.  in.  In  the  writer's  opinion 
these  show  where  the  concrete  failed  in  shear,  or  tension 
due  to  shearing  action.  After  this  failure  of  the  concrete 
the  stirrups  were  brought  into  play,  as  it  would  be  generally 
necessary  for  some  "give"  to  take  place  in  the  concrete  be- 
fore the  U  bars  would  have  a  working  bearing  on  the  hori- 
zontal reinforcing  bars.  This  is  equivalent  to  reinforcing 
a  detail  in  steel  work  with  a  bent  plate  that  will  come  into 
action  after  the  main  detail  fails  or  slips.  Of  course  a 
beam  is  stronger  with  a  system  of  shear  bars  in  close  spac- 
ing than  it  would  be  without  The  writer  believes,  however, 
that  shear  bars  are  neither  an  economic  nor  a  scientific 
method  of  reinforcing  a  beam. 

None  of  the  tests  in  Bulletin  No.  12  failed  by  shear,  and 
some  of  them  stood  double  the  load  required  to  give  the 
first  diagonal  crack  due  to  shear.  It  is  a  precarious  sort 
of  construction,  however,  that  entails  a  system  of  cracks 
in  the  concrete  before  it  can  be  brought  into  play.  A  load 
that  would  produce  the  first  crack  in  the  concrete  would 
not  be  a  safe  load  on  a  beam.  If  a  given  load  causes  cracks 
in  a  beam  it  can  scarcely  be  said  to  be  in  any  better  case 
under  a  great  number  of  repetitions  of  that  load,  than  is 
a  member  subjected  repeatedly  to  stresses  nearly  equal  to 
the  elastic  limit.  We  know  that  the  latter  would  eventu- 
ally cause  failure. 

It  is  common  to  hear  the  system  of  horizontal  bottom 
flange  rods  and  vertical  or  diagonal  shear  rods  sooken  of 
367 


ka  truss  system  and  to  hear  comparisons  made  with  a 
sel  Pratt  truss  or  a  wooden  and  steel  Howe  truss.  Now, 
since,  as  stated,  the  shear  rod  must  have  anchorage  of  some 
sort  outside  of  the  point  where  it  can  take  any  stress,  we 
can  represent  these  so-called  Howe  or  Pratt  trusses  as 
shown  in  Fig.  4  at  (a)  and  (b)  respectively.  The  heavy 
lines  represent  the  compression  members,  or  in  other  words, 
the  concrete  acting  in  compression.  The  light  lines  repre- 
sent the  tension  members,  or  the  shear  rods.  These  are 
good  from  the  point  where  they  are  attached  to  the  rod 
to  the  point  beyond  which  they  have  an  efficient  anchorage. 
It  does  not  take  much  imagination  to  see  what  would 
happen  to  a  truss  on  the  lines  of  either  of  these.  And  yet 
these  are  true  representations  of  just  what  we  find  in  rein- 
forced concrete  design  as  used  in  practice  and  as  sanctioned 
in  some  of  the  best  works  we  have  on  the  subject.  These 
abbreviated  tension  members  must  of  necessity  be  aided  by 
tension  in  the  concrete,  the  most  unreliable  factor  in  its 
strength. 

Fig.  3  at  (rf),  shows  a  beam  reinforced  for  shear  in  a 
manner  that  is  rational  and  meets  all  requirements.  If  this 
beam  were  cracked,  the  rod  could  not  pull  out  because  of 
the  anchorage.  If  the  beam  be  one  in  a  continuous  line, 
the  rod  could  pass  into  the  next  span  for  anchorage,  acting 
in  that  span  at  the  same  time  as  reinforcement  for  the  top 
flange  to  take  the  stress  due  to  continuity.  This  sort  of 
reinforcement  is  needed  in  beams  less  than  i-io  of  the  span 
in  depth. 

To  return  to  a  discussion  of  the  tests  made  at  the  Uni- 
versity of  Illinois.  There  are  some  features  about  the  re- 
sults of  these  tests  that  it  is  instructive  to  note.  Average 
values  do  not  count  for  much  where  there  is  a  wide  range 
of  results.  For  example,  if  there  is  a  difference  of  100  per 
cent  between  the  lowest  and  the  highest  result,  and  if  the 
mean  is  midway  between  these,  a  design  made  on  the  basis 
of  the  mean  value  with  a  factor  of  safety  of  4  will  have 
a  factor  of  safety  of  less  than  3  on  the  basis  of  the  lowest 
value.  Often  there  is  a  difference  of  several  hundred  per 


cent  in  the  result  of  tests  on  such  uncertainties  as  bending 
and  shear  in  wood,  shear  in  concrete,  etc.  Designs  on  the 
basis  of  mean  values  may  thus  have  a  factor  of  safety  that 
is  half  fictitious,  for  the  lowest  value  is  as  apt  to  be  found 
in  the  finished  structure  as  the  highest  or  as  the  mean. 

Among  the  punching  tests  on  plain  plates  there  is  one 
that  shows  a  shearing  strength,  at  first  crack,  of  142  Ib.  on 
1:3:6  concrete.  One  test  on  1:2:4  concrete  shows  213  Ib. 
per  sq.  in.  at  first  crack.  One  recessed  block  of  i  13  :6  con- 
crete shows  258  Ib.  per  sq.  in.  at  first  crack,  and  one  of 
1 :2 :4  concrete  shows  332  Ib.  One  reinforced  recessed  block 
of  1 :3 :6  concrete  shows  496  Ib.  per  sq.  in.  at  first  crack 
and  one  of  1 :2 14  concrete  shows  668  Ib.  One  restrained 
beam  of  1 :2 14  concrete  shows  783  Ib.  per  sq.  in.  at  first 
crack.  These  results  run  from  *A  to  Y$  of  the  ultimate 
shearing  strength  found.  It  may  be  true  that  all  of  these 
low  values  were  the  result  of  tensile  stresses  due  to  beam 
action.  If  this  is  true  in  a  test  where  every  effort  is  made 
to  eliminate  beam  action,  how  can  anything  else  be  ex- 
pected in  practice? 

Turning  now  to  the  ratio  between  ultimate  shear  and 
ultimate  compression  we  find  it  to  be  as  low  as  .37  for  plain 
punched  plates,  .39  for  recessed  blocks,  .67  for  reinforced 
recess  blocks,  and  .44  for  restrained  beams.  In  some  tests 
the  apparent  ultimate  shearing  strength  was  more  than  the 
ultimate  compressive  strength.  This  wide  variation  shows 
the  uncertainty  in  shearing  strength  of  concrete,  to  which 
reference  has  heretofore  been  made. 

A  fair  average  value  for  tension  in  1 :2 14  concrete  is 
about  200  Ib.  per  sq.  in.  Using  i  1-3  times  this  as  a  basis 
for  shear  40  Ib.  and  50  Ib.  per  sq.  in.  are  seen  to  represent 
factors  of  safety  about  6  and  5  respectively.  These  factors 
are  not  any  too  large,  in  view  of  the  uncertainty  exhibited 
in  concrete  in  shear  and  tension,  for  use  in  the  design  of 
beams. 


369 


The  Design  of  Reinforced  Concrete 
Columns. 

The  strength  of  a  plain  concrete  column  is  largely  deter- 
mined by  the  shearing  strength  of  the  concrete.  In  Fig.  I, 
at  (a),  is  shown  a  column  carrying  a  load  P.  If  this  be  re- 
solved into  C  B  and  C  A,  the  latter  will  be  compression  on 
the  surface  M  N  and  the  former  will  be  shear  on  the  same 
surface.  The  angle  y  to  make  the  unit  shear  on  M  N  a 
maximum  will  be  45  deg.  and  the  intensity  of  that  unit 
shear  is  just  half  the  unit  compression  on  the  column.  Two 
planes  of  failure  may  meet  as  at  (b),  forming  a  wedge. 
The  point  of  the  wedge  may  be  crushed,  or  the  wedge  may 
act  to  split  the  column.  This  bulging  or  splitting  action 
is  a  common  failure  in  wooden  columns,  on  account  of  the 
weakness  of  wood  in  shear.  It  is  also  a  typical  form  of 
failure  in  concrete  columns.  The  wedges  or  cones  may 
form  at  the  ends  and  split  or  bulge  the  entire  column.  At 
(c)  is  shown  the  futility  of  reinforcement  with  longitudinal 
rods  of  small  diameter.  These  will  bend  if  the  column 
bulges,  and  will  be  of  little  use.  In  cubes  under  test  the 
cones  will  meet,  either  apex  to  apex  or  base  to  base,  and 


teJ  fbj  (c) 

(FIG.  1.    SHOWING  BULGING  ACTION  IN 
COLUMN. 

only  corners  will  be  flaked  or  spawled  off  by  the  shear, 

leaving  the  core  in  compression;  hence  the  fallacy  of  re- 

370 


lying    on   tests    on   cubes    to    determine   the    compressive 
strength  of  plain  concrete  shafts  or  columns. 

In  laboratory  tests,  plain  concrete  columns  of  5  or  10 
diameters  in  length  will  sustain  moderately  high  compres- 
sive stresses.  This  is  because  of  the  centric  application  of 
the  load.  The  shearing  strength  of  concrete  in  a  plane 
which  is  at  the  same  time  subject  to  compression  is  very 
much  greater  than  if  there  is  tension  instead  of  compres- 
sion, acting  on  that  plane ;  it  is  also  greater  than  if  there  is 
no  stress  normal  to  the  surface.  The  friction  between  the 
surfaces  due  to  the  compressive  strength  adds  an  apparent 
shearing  strength  to  the  actual  shearing  strength  of  the 
concrete.  It  is  also  true  that  columns  reinforced  with  lon- 
gitudinal rods,  in  laboratory  tests,  sometimes  show  mod- 
erately high  compressive  strength.  This  may  also  be  at- 
tributed to  the  fact  that  the  load  is  applied  exactly  in  the 
center  of  the  column. 

Only  a  small  shifting  of  the  load  on  a  plain  concrete  col- 
umn, or  one  reinforced  with  longitudinal  rods,  is  necessary 
to  bring  into  play  the  weakness  of  the  concrete.  When  the 
center  of  gravity  of  the  applied  load  on  a  square  column  is 
more  than  1-6  of  the  diameter  from  the  center,  or  when 
that  on  a  circular  column  is  more  than  ^  of  the  diameter 
from  the  center,  there  will  be  tension  on  the  extreme  fiber 
of  the  column.  The  shearing  strength,  which  is  the  crit- 
ical factor  in  the  strength  of  the  column,  is  immediately 
weakened  when  the  compression  is  removed  and  both  shear 
and  compression  become  of  double  intensity  on  the  other 
side  of  the  column.  The  bulging  action  illustrated  in  Fig. 
I  will  be  augmented  by  eccentric  loading. 

Eccentric  loading  of  columns  in  buildings  is  the  rule  and 
not  the  exception.  In  tests  it  is  the  rule  to  apply  loads 
centrally.  It  is  of  utmost  importance  that  reinforced  con- 
crete columns  be  made  capable  of  resisting  eccentric  loading 
or  flexure. 

Concrete  columns  with  longitudinal  rods  embedded  in 
them  are  not  efficient  and  are  not  rational  design,  for  the 
following  reasons: 

371 


(1)  The  column  is  a  composite  of  steel  and  concrete, 
and  not  a  true  reinforced  concrete  column,  as  the  steel  must 
be  chiefly  in  compression. 

(2)  There  is  no  way  to  determine,  even  approximately, 
the  respective  amounts  of  the  load  that  the  steel  and  the 
concrete  will  bear.    The  use  of  the  moduli  of  elasticity  of 
the  two  materials  is  no  aid,  on  account  of  the  fact  that  the 
concrete  tends  to  shrink  and  shorten,  leaving  the  steel  rods 
longer  than  the  normal  unstressed  concrete. 

(3)  If  the  rods  are  near  the  surface  of  the  concrete, 
they  can  more  easily  break  out  under  the  bowing  action  of 
direct  compression  or  the  bulging  action  of  diagonal  shear. 

(4)  If  the  rods  are  near  the  center  of  column,  they  will 
be  of  no  aid  to  resist  flexural  stresses  due  to  horizontal 
forces  or  to  eccentric  loading. 

(5)  Longitudinal  rods  offer  little  or  no  resistance  to 
longitudinal  splitting  or  bulging  of  the  column. 

(6)  The  rods  cannot  take  diagonal  shear  without  over- 
stressing  the  concrete. 

The  assumption  that  they  can  take  shear,  in  amounts  of 
anywhere  near  the  capacity  of  steel  to  carry  shear,  is  sim- 
ply untenable  and  absurd,  in  spite  of  recognition  in  build- 
ing codes  and  regulations.  If,  for  example,  we  assume  a 
shear  of  12,000  Ib.  in  a  rod  I  in.  sq.,  there  must,  of  neces- 
sity, be  a  bending  moment  in  the  rod.  Now  the  square  rod, 
at  24,000  Ib.  extreme  fiber  stress,  would  take  a  bending 
moment  of  4,000  in.-lb.  The  lever  arm  of  the  12,000  Ib. 
would  then  have  to  be  only  1-3  of  an  in.  The  force  of 
12,000  Ib.  applied  on  the  side  of  a  square  rod  in  a  length 
of  1-3  of  an  in.,  or  on  several  times  this  length,  is  beyond 
the  power  of  concrete  to  withstand. 

(7)  A  plane  of  cleavage,  especially  if  it  be  a  sloping 
one,  such  as  a  joint  left  where  pouring  of  concrete  ceases 
for  a  while,  will  leave  a  weak  section  and  vitiate  to  a  large 
extent  the  factor  of  safety. 

Comparison  of  a  reinforced  concrete  column  with  a  steel 
column  as  a  basis  of  design  is  misleading,  because  of  the 
fact  that  steel  is  very  strong  in  tension  and  therefore  capable 
372 


of  resisting  bending  stresses.  Cast  iron  columns  were  for- 
merly proportioned  on  the  basis  of  11,300  Ib.  per  sq.  in. 
(reduced  for  length).  Full  size  tests  imade  some  years  ago 
(see  Eng.  Record,  June  n,  1898)  showed  this  unit  to  be 
too  high  and  that  a  proper  unit  is  about  7,600  Ib.,  reduced 
for  length  of  column.  The  compressive  strength  of  cast 
iron  in  short  blocks  is  about  100,000  Ib.  per  sq.  in.,  but  on 
account  of  the  low  tensile  strength,  and  consequent  low 
shearing  strength,  the  safe  unit  in  columns  has  but  a  remote 
relation  to  the  compressive  strength  in  short  test  pieces. 
An  exactly  similar  condition  exists  in  columns  of  plain  con- 
crete or  of  concrete  that  is  not  reinforced,  with  a  view  of 
relieving  it  of  all  tensile  strains  and  of  excessive  shearing 
strains. 

Practical  experience  has  proven  the  inability  of  concrete 
columns  in  which  small  rods  are  embedded  to  carry  heavy 
loads.  The  practical  experience  referred  to  is  the  failures 
of  buildings  that  have  recently  occurred. 

When  a  small  section  of  a  building  falls,  the  failure  may 
be  attributed  to  a  local  cause,  generally  a  fault  or  defect 
in  the  beams.  When  a  general  collapse  of  a  large  section 
of  a  building  occurs,  it  is  probable  that  the  failure  is  due  to 
weakness  in  the  columns.  If  one  beaim  fails,  it  ought  not 
to  bring  down  with  it  much  of  the  rest  of  the  structure. 
When  a  column  fails,  it  lets  down  a  large  section  of  the 
floor;  and  if  the  other  columns  have  the  same  weakness 
they  will  follow.  The  great  weight  falling  on  lower  floors 
will  overload  these  by  the  shock  and  add  to  the  extent  of 
the  failure. 

In  a  failure  that  occurred  some  years  ago,  the  reinforced 
concrete  roof  of  a  large  building  fell  in  on  account  of  the 
concrete  not  having  set  before  the  forms  were  removed. 
The  weather  was  very  cold,  and  the  concrete  froze  instead 
of  setting.  This  great  weight  falling  did  not  affect  the 
floors  below  and  did  not  affect  the  columns  supporting 
them.  The  columns  had  steel  spirals  and  longitudinal  rods 
wired  to  them.  The  beams  and  girders,  while  not  ideal  in 
design,  had  rods  across  the  supports  to  tie  them  together. 
373 


Recently  two  large  buildings  being  constructed  exhibited 
such  serious  weakness  that  large  sections  of  them  col- 
lapsed. The  columns  of  these  buildings  were  made  of  con- 
crete with  some  longitudinal  rods  through  them.  The  safe 
strength  of  such  columns  cannot  be  said  to  be  intimately 
related  to  the  compressive  strength  of  concrete  in  cubes; 
and  yet  the  unit  compression,  in  some  cases,  for  dead  load 
alone,  was  in  the  neighborhood  of  %  of  the  ultimate  com- 
pressive strength  of  concrete  cubes.  Compare  the  ulti- 
mate strength  of  cast  iron  with  the  unit  used  in  a  properly 
designed  column. 

Square  concrete  columns  in  which  longitudinal  rods  are 
placed  near  the  corners,  and  these  rods  tied  together  by 
straight  rods  or  bands,  are  a  step  in  the  right  direction. 
These  horizontal  ties  will  resist  the  bursting  or  bulging 
tendency  of  the  load;  but  as  this  tendency  is  in  all  direc- 
tions, it  will  act  to  make  the  square  formed  by  these  ties 
into  a  circle.  The  outward  force  at  the  side  of  the  square 
is  not  adequately  resisted.  The  metal  is  not  economically 
disposed.  It  is  somewhat  analogous  to  a  square  vessel  con- 
taining a  liquid.  A  round  or  cylindrical  vessel  will  require 
much  less  metal  and  will  be  more  rigid. 

It  follows,  then,  that  rational  design  of  reinforced  con- 
crete columns  demands  not  only  longitudinal  reinforce- 
ment to  take  flexural  stresses,  but  circular  reinforcement 
to  take  the  bursting  or  bulging  forces  due  to  diagonal 
shear.  Columns  so  designed  have  proven  under  test  to  be 
the  strongest  of  all  known  forms  of  reinforced  concrete 
columns. 

A  steel  cylinder  rilled  with  concrete  would  meet  the  re- 
quirements most  completely.  Concrete  will  stand  very 
great  pressure  thus  confined,  even  to  the  extent  of  being 
forced  out  of  shape  and  still  retaining  its  adhesion.  Col- 
umns so  designed,  however,  do  not  seem  to  be  suitable  for 
ordinary  construction. 

Flat  bands  in  hoops  or  in  a  coil,  having  a  diameter 
somewhat  less  than  the  column,  so  that  they  will  be  sur- 
rounded by  concrete,  in  conjunction  with  longitudinal  rods, 
374 


would  seem  to  be  a  near  approach  to  the  cylinder  filled  with 
concrete.  Concrete,  however,  will  not  grip  flat  bands  as 
it  will  round  and  square  rods  and  will  not  adhere  as  well 
to  them.  There  will  be  the  tendency  of  the  concrete  to 
break  off  outside  of  the  bands,  especially  if  the  space  be- 
tween bands  is  small.  Columns  thus  reinforced  will  take 
very  heavy  loads. 

A  practical  objection  to  bands  for  reinforcing  hoops  or 
spirals  is  that  it  is  more  difficult  to  puddle  the  concrete 
around  them  and  make  it  fill  the  voids  outside  of  the  bands. 
Another  objection  is  the  greater  liability  of  concrete  to 
break  off  the  flat  bar  under  the  heat  of  a  fire  and  thus  ex- 
pose the  steel  to  the  heat.  Bands  would  have  to  be  welded, 
and  a  weld  in  steel  is  more  or  less  of  an  uncertainty. 

A  good  and  efficient  column  is  made  by  reinforcing  a 
round  or  an  octagonal  column  with  a  coil  made  of  a  square 
rod  and  with  8  longitudinal  square  rods  wired  to  the  same, 
just  inside  of  the  coil.  The  purpose  of  the  longitudinal 
rods  is  to  take  flexural  stresses,  that  is,  to  relieve  the  con- 
crete of  longitudinal  tensile  stresses  due  to  any  side  force 
or  any  tendency  to  bow  at  the  middle  of  the  height  of  the 
column.  The  steel  thus  used  is  rationally  employed,  as  it 
takes  tension  that  would  otherwise  come  on  the  concrete. 
These  steel  rods  should  not  be  counted  upon  to  take  any  of 
the  direct  load  of  the  column,  because  of  the  fact  that  tests 
show  that  such  rods  alone  in  a  concrete  column  offer  little 
or  no  assistance  to  the  concrete. 

When  a  concrete  column  is  under  compression,  its  length 
is  diminished  and  its  diameter  is  increased  somewhat.  The 
steel  coils  come  into  play  by  this  tendency  of  the  column 
to  increase  in  diameter  and  are  therefore  in  tension. 

In  a  series  of  tests  made  by  M.  Considere,  hooped  con- 
crete prisms  showed  very  high  compressive  strengths. 
They  further  showed  a  regularity  in  the  matter  of  breaking. 
Plain  concrete  prisms  broke  suddenly,  whereas  hooped 
prisms  would  hold  together  after  partial  failure  had  oc- 
cured  and  would  sustain  great  loads  in  this  condition.  The 
immense  advantage  of  this  toughness  in  a  column  is  very 
375 


manifest,  and  it  is  the  strongest  argument  for  hooped  col- 
umns. It  is  plain  that  partial  failure  in  a  column  with  only 
small  longitudinal  rods  in  it  would  be  a  matter  of  very 
serious  moment.  The  possibility  of  shrinkage  cracks  in 
concrete  must  always  be  kept  in  mind.  Longitudinal  rods 
in  a  column  offer  no  safeguard  whatever  against  such 
cracks,  whereas  in  columns  reinforced  with  a  spiral  or 
hoops  in  addition  to  longitudinal  rods,  cracks  are  of  no 
serious  consequence. 

Tests  made  at  the  Watertown  Arsenal  in  1906  on  col- 
umns 10  to  12  in.  in  diameter  and  8  ft.  in  height,  corrobo- 
rate the  results  of  the  tests  made  by  Considere.  They  show, 
.  in  general,  that  as  hoops  approach  each  other  the  ultimate 
strength  of  the  column  is  very  greatly  increased. 

A  basis  for  determining  the  size  of  the  rods  in  the  coil 
is  found  in  analogy  of  the  column  to  a  tube  containing  a 
liquid  under  pressure.  The  stress  in  the  rod  corresponds 
to  the  annular  tension  in  the  walls  of  the  tube.  Under  the 
ultimate  pressure  the  concrete  would  be  in  a  disintegrated 
state  and  would  resemble  sand.  In  this  condition  it  would 
exert  a  lateral  pressure,  but  not  a  pressure  equal  to  that 
exerted  by  a  liquid  under  the  same  force.  M.  Considere 
found  that  the  lateral  pressure  was  10-48  of  that  of  the 
longitudinal  pressure  in  disintegrated  concrete  and  in  sand. 

If,  at  failure,  there  is  a  lateral  unit  pressure  correspond- 
ing to  10-48  of  the  compression  in  the  direction  of  the  axis 
of  the  column,  we  can  assume  that  the  same  relation  holds 
true  under  safe  loads.  Whether  or  not  it  does  hold  true  is 
of  little  consequence,  so  long  as  it  is  certain  that  this  as- 
sumed stress  in  the  steel  is  not  exceeded,  it  is  a  sound  basis 
for  finding  the  size  of  coil  for  the  following  reason: 

Suppose  we  have  a  column  which,  under  tests,  has  dis- 
integrated so  as  to  be  practically  like  sand  in  the  matter  of 
exerting  lateral  pressure.  The  lateral  unit  pressure  will 
be  10-48  of  the  unit  compression,  and  this,  on  rods  strained 
to  their  ultimate  usefulness  (the  elastic  limit,  as  usually 
conceded  in  reinforced  concrete  work),  would  give  a  con- 
dition where  the  concrete  and  steel  are  consistently  propor- 
376 


tioned.  Now,  if  a  factor  of  safety  be  applied,  both  to  the 
stress  in  rods  and  the  compression  in  concrete,  the  consis- 
tency of  the  design  is  maintained,  though  the  actual  stress 
in  the  steel  is  not  thereby  definitely  determined.  Suppose 
that  it  were  known  that  the  rods  in  some  construction  were 
not  stressed  much  until  9-10  of  the  ultimate  load  were  upon 
it,  and  that  they  then  suddenly  received  their  load.  We 
would  not  have  a  consistent  design  unless  the  ultimate 
strength  of  the  rods  corresponds  with  the  ultimate  strength 
of  the  structure,  in  spite  of  the  fact  that  the  actual  stress 
in  the  rods  under  a  safe  load  on  the  structure  may  be  small 
and  indeterminate.  It  is  conceivable  that  in  a  reinforced 
concrete  beam  the  concrete,  in  some  cases,  takes  nearly  all 
of  the  tension  up  to  its  ultimate  strength,  and  that  in  the 
case  of  stress  above  its  ultimate  strength  the  stress  at  the 
crack  is  imparted  to  the  steel  in  its  entirety.  This  may  be 
the  explanation  of  the  fact  that  beams  sometimes  show  no 
cracks  on  the  tension  side  under  stresses  which,  if  con- 
centrated in  the  reinforcing  steel,  represent  elongations 
that  would  overtax  the  integrity  of  the  concrete.  Granting 
for  the  sake  of  argument  that  this  is  the  case  and  that 
under  safe  loads,  with  perfect  concrete,  the  steel  is  under 
very  little  stress,  and  that  the  concrete  in  tension  is  doing 
practically  all  of  the  work;  it  can  by  no  means  be  con- 
strued as  warrant  for  proportioning  the  steel  for  this  ideal 
condition.  Laboratory  tests,  both  on  beams  and  columns, 
lead  to  conclusions  such  as  this,  because  of  the  ideal  con- 
ditions that  prevail  in  the  manufacture  and  testing  of  speci- 
mens. 

Practical  design  must  take  into  account  actual  conditions 
in  practical  construction  and  practical  defects  that  are  liable 
to  be  incorporated  in  a  structure. 

In  a  hooped  column  or  one  reinforced  with  a  spiral,  a 
condition  may  exist  that  is  analogous  to  that  just  postu- 
lated of  a  beam.  It  is  therefore  in  reason  to  proportion 
the  steel  in  a  column  as  though  it  took  all  of  the  tensile 
stress  tending  to  bulge  or  burst  the  column,  just  as  we 
proportion  the  steel  in  a  reinforced  concrete  beam  to  take 
377 


all  of  the  tensile  stresses  that  might  come  on  the  concrete. 

An  assumption,  such  as  that  made  in  a  recent  work  on 
reinforced  concrete,  namely,  that  a  column  has  a  compres- 
sive  strength  due  to  the  strength  of  the  concrete  alone  in 
compression,  and  another  compressive  strength  due  to  the 
hoops  or  spirals,  is  untenable.  Both  of  these  supposed 
joint  strengths  would  break  down  at  once.  They  are  sim- 
ply different  phases  of  the  same  thing.  The  plain  concrete 
alone  would  be  weak  as  a  column,  and  the  hoops  or  spiral 
alone  would  be  absolutely  useless  as  a  column.  The  hoops 
supply  what  the  concrete  needs  to  hold  it  together.  The 
concrete  between  the  hoops  is  simply  plain  concrete.  No 
quality  is  imparted,  by  the  reinforcement,  to  the  concrete 
between  the  coils  that  it  does  not  possess  in  short  blocks 
or  discs.  Hence  a  proper  unit  load  would  be  a  safe  value 
for  compression  on  short  prisms  of  plain  concrete.  If  the 
concrete  be  the  standard  1 :2 14  concrete  generally  used  in 
reinforced  concrete  work,  a  proper  unit  in  compression 
would  be  between  500  and  600  Ib.  per  sq.  in. 

It  is  true  that  in  columns  where  the  hoops  are  spaced 
close  together  the  compressive  strength  of  columns  under 
test  runs  up  to  5,000  and  6,000  Ib.  per  sq.  in.,  just  as  thin 
discs  of  concrete  would  show  correspondingly  high  unit 
strength.  Close  spacing  of  hoops,  however,  entails  prac- 
tical difficulties  in  puddling  the  concrete  around  the  bars, 
and  the  almost  continuous  cylinder  of  metal  forms  a  cleav- 
age surface  from  which  the  concrete  is  apt  to  break  away. 
This  last  might  result  from  ordinary  changes  of  temper- 
ature, and  would  be  a  strong  probability  in  the  case  of  a 
fire. 

In  the  work  on  reinforced  concrete  above  referred  to, 
the  author,  while  rinding  a  compressive  strength  in  a  set  of 
loose  hoops,  or  a  flimsy  coil,  apart  from  that  of  the  con- 
crete which  they  are  intended  to  reinforce,  and  in  addition 
to  the  strength  of  that  concrete,  shows  his  lack  of  confi- 
dence in  his  formula  by  throttling  his  unit  value  with  an 
empirical  constant  that  almost  cuts  it  in  half. 

If  we  assume  a  safe  load  of  550  Ib.  per  sq.  in.  and  a 

378 


lateral  pressure  of  10-48  of  this  in  intensity,  we  have  a 
basis  for  the  determination  of  the  tension  on  a  coil.  Let 
the  pitch  of  the  coil  be  l/%  of  the  diameter  of  the  column 
and  let 

D  •=.  diameter  of  column  in  inches; 

d  =  diameter  of  square  steel  rod  in  the  coil,  in  inches. 

Equating  the  equivalent  fluid  pressure  on  the  rod  to  its 
tension  at  12,500  Ib.  per  sq.  in.,  we  have 

650X->|X^4=12,500*> 
Solving  we  find 

d=~42 

If  we  make  the  diameter  of  the  coil  %  of  that  of  the 
column,  and  the  diameter  of  the  square  rod  of  which  the 
coil  is  made  1-40  of  the  diameter  of  the  column,  we  shall 
have  close  to  12,500  Ib.  per  sq.  in.  on  the  steel. 

For  the  8  rods  which  run  the  length  of  the  column  we 
may  assume  the  same  lateral  pressure  and  proportion  the 
rods  to  take  that  pressure.  Assuming  that  they  would  act 
to  resist  the  outward  pressure  of  the  disintegrated  concrete, 
at  the  ultimate  strength  of  the  column,  we  can  make  the 
rods  of  a  diameter  that  they  would  take  the  stresses  in 
bending,  at  a  safe  unit,  due  to  a  lateral  pressure  10-481  of 
550  or  115  Ib.  per  sq.  in.  The  outward  force  per  inch  in 
the  length  of  rod  is  115  X  ic  X  D  -f-  8.  The  clear  span  is 
l/%  of  D  less  1-40  D  =  i-io  of  D.  As  the  rods  are  fixed 
ended,  the  bending  moment  is  1-12  of  w  f,  or 


Equating  this  to 

I25ood/8  -4-  6 

the  resisting  moment  of  a  square  rod  of  a  diameter  d'  we 
obtain 


As  this  is  close  to  1-40  of  the  diameter  of  the  column,  we 


may  use  the  same  size  of  square  rods  as  that  used  in  the 
coil. 

It  is  recommended,  therefore,  that  reinforced  concrete 
columns  be  made  round  or  octagonal  and  that  the  entire 
area  of  the  circle  or  octagon  be  considered  as  taking  the 
load;  also  that  the  reinforcement  be  made  of  a  coil  of 
square  steel  rods  of  a  diameter  one-fortieth  that  of  the 
column;  also  that  just  inside  of  this  coil  eight  rods  of  the 
same  diameter  be  wired  to  the  coil.  At  the  end  of  a  coil 
the  rod  should  lap  a  half  a  circle,  as  this  would  be  about  55 
diameters. 

The  unit  of  550  Ib.  sq.  in.  would  be  used  for  lengths  up 
to  10  diameters.  Between  10  and  25  diameters  the  allowed 
unit  pressure  would  be  found  by  the  following  formula: 


where  p  =  allowed  pressure  per  sq.  in., 

/  =  length  in  inches. 

D  =  diameter  in  inches. 

Columns  more  slender  than  1-25  of  their  length  should 
be  avoided.  The  same  reinforcement  should  be  used  in 
all  columns  of  a  given  diameter,  so  that  flexural  and  ec- 
centric stresses  will  be  taken  care  of  in  long  columns. 

The  'practice  of  using  such  units  as  1,000  Ib.  per  sq.  in. 
on  concrete  in  columns  is  fraught  with  great  danger.  Lab- 
oratory tests  on  carefully  prepared  specimens  under  per- 
fectly central  loading  are  not  proper  criteria  for  the  de- 
sign of  columns  that  have  to  take  eccentric  loads  and  in 
addition  have  to  resist  the  wind  loads  tending  to  sway  a 
building.  A  quality  in  columns  that  is  very  essential,  es- 
pecially in  high  buildings,  is  toughness.  High  buildings 
of  12  to  15  or  more  stories  require  very  large  columns  in 
the  lower  stories,  at  units  that  are  proper  for  concrete; 
hence  some  other  kind  of  column  may  better  be  employed 
for  the  stories  where  very  heavy  loads  are  carried.  A 
suitable  column  would  be  of  steel  latticed  on  two  sides 
and  filled  and  surrounded  with  concrete.  Such  a  column 
380 


could  be  made  of  two  channels,  either  rolled  or  built. 
Shelves  could  be  riveted  on  to  support  the  reinforced  con- 
crete girders,  and  the  lattice  could  be  left  out  where  the 
girder  passes  through  the  column.  If  girders  or  beams 
connect  into  all  four  sides  of  the  column,  brackets  could 
be  riveted  on  the  side  of  the  channels  and  holes  left  in 
the  web  for  reinforcing  rods  to  go  through  the  column. 
Another  kind  of  steel  column  could  be  made  of  four  an- 
gles set  back  to  back,  but  separated  so  that  the  reinforced 
concrete  beams  and  girders  can  pass  between.  These  an- 
gles could  be  connected  by  batten  plates  at  intervals.  Such 
a  column,  while  it  is  objectionable  in  a  plain  steel  column 
on  account  of  having  no  web  to  transfer  shear  from  one 
part  of  the  column  to  another,  would  not  have  this  fault, 
if  it  were  completely  surrounded  with  good  concrete. 

Steel  columns  such  as  those  referred  to  could  be  merged 
into  reinforced  concrete  columns  by  allowing  the  coil  of 
the  latter  to  pass  down  over  the  steel  section  for  a  dis- 
tance. 

For  a  unit  load  on  a  steel  column  surrounded  and  filled 
with  concrete  a  value  much  higher  than  for  a  plain  steel 
column  of  the  same  section  could  safely  be  employed. 
Units  between  14,000  and  16,000  Ib.  per  sq.  in.  would  not 
be  excessive,  if  the  diameter  of  the  concrete  shaft  is  not 
less  than  a  tenth  or  a  twelfth  of  the  clear  height.  A 
division  of  the  load  between  the  concrete  and  the  steel 
is  not  to  be  recommended  because  of  the  impossibility 
of  determining  how  much  each  will  take. 

^I  Jcat  , 


381 


Design  of  Dams  and  Use  of  Concrete 
Therein. 

Structures  for  the  impounding  of  water  are  among  the 
oldest  of  engineering  works.  The  forces  acting  upon  dams 
are  in  many  ways  among  the  simplest  and  most  easily  de- 
termined. It  is  a  sad  commentary  on  modern  engineering 
to  say  that  some  of  the  worst  calamities  in  which  man  was 
a  causal  agency  have  been  the  result  of  the  overthrow 
of  structures  whose  stability  is  a  matter  of  the  most 
elementary  calculation  and  the  forces  against  which  are 
completely  determinate. 
The  writer  makes  this  preface  to  the  present  article  in 

i  order  to  emphasize  a  factor  that  he  believes  to  be  the 
cause  of  many  failures  of  dams,  and  because  in  all  tech- 

|  nical  literature  there  is  scarcely  a  mention  made  of  this 

i  factor.  The  factor  referred  to  is  none  other  than  the 
floating  or  buoyant  power  of  the  impounded  water.  An 
offhand  answer  to  this  would  be  that  water  will  not  tend 
to  float  anything  not  submerged.  It  is  practically  im- 
possible to  seal  the  up-stream  side  of  a  dam  against  the 
admission  of  water  under  the  dam,  and  the  thinnest  sheet 
of  water,  entering  the  finest  crevice,  exerts  the  same  up- 
lifting tendency  on  the  under  side  of  a  dam  that  would 
be  exerted  in  a  large  crack.  Even  if  this  upward  pressure 
on  the  under  side  of  the  dam  be  diminished  uniformly  to 
zero  at  the  down-stream  edge  of  the  dam,  where  the  water 
emerges,  the  effect  of  the  pressure  on  the  stability  of  the 

j  dam  is  the  same  as  though  the  pressure  of  the  full  head 

i  were  maintained  for  the  entire  width  of  the  dam.  It  is 
true  that  this  pressure  can  be  diminished  by  under-drainage, 

j  but  this  would  be  apt  to  waste  much  water,  and  it  is  seldom 
resorted  to. 

Much  has  been  said  of  the  suction  exerted  on  the  down 
stream  face  of  a  dam  when  water  is  spilling  over  it,  in 
attempted  explanation  of  failures.  It  is  a  dangerous  theory 

i  that  magnifies  non-essentials  and  overlooks  essentials. 
There  is  a  small  negative  pressure  under  the  falling  sheet 
of  water,  probably  amounting  to  as  much  as  a  strong  wind, 


in  some  cases,  or  even,  in  large  dams,  to  a  foot  or  two  of 
water  on  a  portion  of  the  face.  But  it  has  never  been 
shown  that  this  negative  pressure  actually  equals  the  drop 
of  the  water  head  from  the  level  of  the  main  body  to  a 
point  vertically  over  the  crest  of  dam.  Now  it  is  this 
head  of  the  main  body  of  the  water  that  should  be  used 
in  proportioning  the  dam;  and,  as  the  hydrostatic  pressure 
on  the  back  of  the  dam  is  measured  by  the  head  at  the 
crest,  there  is  this  margin  of  the  difference  between  these 
two  heads  that  will  be  ample  to  cover  both  the  negative 
pressure  on  the  face  and  the  effect  of  the  small  flow  in 
the  main  body.  The  effect  of  the  flow  is  to  add  pressure 
on  the  back  of  the  dam  above  that  which  would  be  pro- 
duced by  the  static  head  just  over  the  crest,  but,  as  only 
the  upper  strata  of  the  water  are  in  motion,  the  water  has 
a  velocity  head  or  dynamic  head  only  to  a  very  limited 
degree. 

Impact  of  water  on  a  dam  is  another  element  whose  im- 
portance is  probably  overestimated.  For  a  large  body  of 
water  to  impinge  on  the  back  of  a  dam  it  would  have  to 
advance  with  a  front  nearly  vertical  into  an  empty  reser- 
voir. This  would  not  even  be  approached  except  by  the 
failure  of  a  dam  at  a  higher  elevation.  Floods  have  the 
natural  effect  of  increasing  the  head  and  the  static  pressure 
on  the  back  of  the  dam,  and  if  the  maximum  level  of  water 
is  known  and  the  dam  designed  therefor,  there  should  be 
no  more  fear  of  a  dam  failing  than  of  a  railroad  bridge 
failing  when  it  receives  its  full  calculated  maximum  load. 

The  foregoing  is  not  written  to  show  that  the  design  of 
dams  is  the  simplest  of  operations.  There  are  many  dif- 
ficult problems  in  connection  with  their  design,  especially 
in  such  construction  as  earth  dams  and  rubble  dams.  The 
greatest  problem,  however,  is  generally  to  come  within  the 
appropriation,  and  too  often  this  is  done  by  ignoring  the 
most  potent  factor  opposing  the  stability  of  the  dam. 

In  the  design  of  dams  the  factor  of  safety,  with  which 
we  are  familiar  in  other  branches  of  designing,  has  scarcely 
any  meaning,  at  least  as  regards  stability  against  over- 
turning. With  those  structures  where  the  factor  of  safety 

383 


plays  an  important  part  there  can  not  be  said  to  be  a  point 
where  a  structure  ceases  to  be  safe  and  becomes  unsafe 
or  vice  versa.  In  stability  against  overturning,  however, 
there  is  a  distinct  line  on  one  side  of  which  a  structure  is 
stable  and  on  the  other  side  of  which  it  is  unstable.  There 
is  a  popular  notion,  owing  its  existence  to  public  school 
"philosophy,"  that  an  object  cannot  be  overturned  until 
the  center  of  gravity  falls  without  the  base.  This  is  quite 
true  of  miniature  objects,  but  a  great  wall  of  stone  stood 
upon  its  corner  would  be  disintegrated  by  the  heavy  pres- 
sure on  that  corner.  With  all  possible  external  pressures 
considered  and  the  resultant  of  these  pressures  and  the 
weight  of  the  dam  falling  within  or  at  the  edge  of  the 
middle  third  of  the  base,  the  dam  will  be  stable.  If  the 
resultant  pressure  falls  without  the  middle  third  of  the 
base,  the  dam  will  not  be  stable,  as  it  will  have  a  tensile 
or  uplifting  force  sufficient  to  overcome  its  own  weight  at 
the  upstream  edge  whenever  the  extreme  condition  is 
reached.  This  rocking  of  the  structure  is  a  distinct  con- 
dition of  instability.  Opening  of  the  joints  on  the  up 
stream  side  of  the  dam  is  a  menace  to  its  stability,  because 
it  allows  water  at  high  pressure  to  get  beneath  the  masonry. 
This  water  acts  as  a  wedge  to  penetrate  further.  If  the 
dam  is  not  calculated  to  resist  this  lifting  or  buoyant  pres- 
sure, its  stability  is  seen  to  depend  upon  the  sealing  of  the 
upper  face  against  the  admission  of  the  water.  Leaking 
of  reservoirs  is  too  common  an  occurrence  to  need  any 
emphasis.  That  dams  should  be  built,  as  they  sometimes 
are,  whose  stability  depends  upon  their  watertightness, 
seems  incredible,  unless  it  is  the  result  of  ignorance.  This 
latter  assumption  is  probably  not  far  from  the  truth  in 
view  of  the  paucity  of  information  in  technical  works  on 
the  subject  heretofore  alluded  to. 

Barring  dams  that  are  built  in  the  form  of  arches,  that 
is,  with  a  horizontal  curve  in  plan,  dams  are  usually  built 
of  a  few  general  shapes.  As  the  weight  of  water  is  uni- 
formly about  62.5  Ib.  per  cubic  foot  and  that  of  masonry 
is  generally  about  150  Ib.  per  cubic  foot,  it  Is  a  simple 
matter  to  determine  a  ratio  of  base  to  a  height  that  will 
384 


resist  all  possible  water  pressure.  It  is  also  a  simple 
matter  to  try  any  dam  of  known  dimensions  and  see 
whether  this  ratio  obtains. 

In  order  to  judge  of  the  stability  of  a  dam  of  ordinary 
cross  section  the  ratio  of  depth  to  height  will  be  de- 
termined for  a  dam  of  rectangular  cross  section  capable 
of  resisting  only  the  horizontal  pressure  against  the  wetted 
face,  neglecting  in  this  calculation  the  pressure  on  the  un- 
der side  of  the  rectangle. 

The  unit  pressure  of  water  in  every  direction  is  the  same 
at  a  given  depth,  and  in  amount  is  equal  to  the  weight  of 
a  column  or  prism  of  water  whose  cross  section  is  unity 
and  whose  length  is  the  depth  below  the  free  surface  of  the 
water.  Another  principle  of  the  pressure  of  fluids  is  that 
it  is  normal  to  the  surface  against  which  it  is  exerted. 
The  determination  of  the  stability  of  a  dam  amounts,  there- 
fore, to  finding  its  ability  to  resist  easily  determined  forces. 
Assuming  w  to  be  the  weight  per  cubic  foot  of  water,  the 
horizontal  pressure  per  square  foot  on  a  vertical  wall  at 
a  depth  h  below  the  surface  of  water  is  wh.  The  pressure 
increase  directly  as  the  depth,  so  that  the  triangle  of  Fig. 
i  represents  the  forces  acting  upon  the  wall  or  dam.  The 
center  of  gravity  of  this  pressure  is  one-third  of  the  height 
from  the  base,  and  the  amount,  for  one  foot  of  length  of 
the  dam,  is  the  area  of  the  shaded  triangle,  or  wh?-z-2. 
The  overturning  moment  about  the  base  of  dam  is 

2        ~3 6~~ 

This  moment  must  be  resisted  by  the  weight  of  the  dam, 
and  in  order  that  there  be  no  tension  on  the  masonry  the 
resultant  of  the  horizontal  force  and  the  weight  of  the 
dam  must  fall  within  the  middle  third  of  the  base.  The 
lever  arm  of  the  weight  of  the  wall  must  therefore  not 
exceed  one-sixth  of  the  base.  The  moment  of  stability 
for  one  foot  of  length  of  the  dam  is  then  Wtfh  -+•  6,  where 
W  is  the  weight  per  cubic  foot  of  the  masonry.  Equating 
the  overturning  moment  and  the  moment  of  stability,  and 
solving  we  have 

385 


rvh 


FIG    1 


rfi  to 


FIG.  2. 


FIG.  3. 


FIG.  4. 


62        TV 

Using  ISO  and  62.5  as  the  weights  per  cubic  foot  of 
masonry  and  water  respectively  we  find  that  the  base  should 
be  .65  times  the  height. 

A  dam  just  capable  at  any  horizontal  section  of  resisting 
the  static  pressure  of  water  whose  surface  is  at  the  level 
of  the  top  of  the  dam  would  be  triangular  in  section.     In 
Fig.  2  we  have  for  the  equation  between  the  overturning 
moment  and  the  moment  of  stability  the  following: 
wy2  _  Wx'^y 
6  6 

From  which  we  have 


Hence  the  width  of  the  dam  at  the  base  should  be  about 
.65  times  the  height.  This  is  seen  to  be  the  same  as  for 
the  rectangular  wall,  though  the  amount  of  masonry  is 
only  one-half  as  great.  The  reason  that  the  moment  of 
stability  of  the  triangular  wall  is  as  great  as  that  of  the 
rectangular  wall  is  because  the  center  of  gravity  of  the 
triangle  that  is  cut  away  is  directly  over  the  center  of 
moments. 

A  dam  would  of  course  not  come  to  a  point  at  the  top 
but  would  have  some  width.  Masonry  added  to  increase 
the  width  at  the  top  is  well  placed,  as  it  increases  the  mo- 
ment of  stability.  A  form  of  cross  section  very  often 
used  has  the  down  stream  face  curved,  as  in  Fig.  3.  This 
does  not  waste  masonry  in  the  third  of  the  base  where 
weight  does  not  count  for  anything  in  stability.  This  toe 
of  the  dam  must,  however,  be  strong  enough  to  resist  the 
forces  induced  by  the  tendency  to  overturn. 

Turning  now  to  a  consideration  of  the  proportions  of  a 
dam  that  will  resist  riot  only  the  horizontal  pressure  of 
the  water  but  also  the  upward  pressure  from  beneath,  we 
have  a  representation  in  Fig.  4  of  the  forces  acting  on  such 
a  dam.  We  might  assume  that  the  pressure  of  the  water 
beneath  the  dam  gradually  diminishes  as  it  works  its  way 

387 


toward  the  toe  of  the  dam.  The  lower  shaded  triangle 
would  represent  the  upward  forces  against  the  base  of  the 
dam.  It  will  be  seen  that  the  moment  of  a  rectangle  of 
altitude  wh  about  the  center  of  moments  is  the  same  as  that 
of  the  triangle  shown,  hence  it  is  immaterial  whether  or  not 
we  assume  a  diminution  of  pressure. 

The  total  overturning  moment  equated  to  the  moment 
of  stability  gives  us. 


Using  the  same  weights  as  before  for  water  and  masonry 
ve  have 

"F       7~* 

The  width  of  the  dam  at  its  base  should  therefore  be. 
about  .85  times  the  height.  Of  course  making  the  cross 
section  of  the  shape  shown  in  Fig.  3  will  increase  the 
moment  of  stability,  and  the  base  need  not  be  quite  so  wide. 
On  the  other  hand  if  a  height  of  water  greater  than  the 
trest  of  the  dam  is  anticipated,  as  is  very  often  the  case, 
the  above  relation  would  not  be  sufficient. 

This  ratio  of  height  to  base  is  derived  merely  to  show 
iHiat  should  be  the  approximate  relation  for  a  solid  masonry 
dam  capable  of  resisting  all  of  the  possible  forces  against 
h.  There  are  not  many  dams  that  have  a  width  of  base 
.85  of  their  altitude  and  there  are  not  many  that  are  so 
thoroughly  underdrained  as  to  make  this  width  unnecessary. 
A  builder  may  take  long  chances  on  the  probability  of  an 
office  building  or  a  highway  bridge  never  receiving  its 
load  and  be  comparatively  safe.  But  the  pressure  of  water 
is  something  sure  and  determinate,  and  the  integrity  of 
a  dam  is  something  that  ought  not  to  be  trifled  with. 

If  the  slope  of  a  solid  dam  be  made  on  the  upstream  face, 
'tfrhile  the  pressure  of  the  water  will  act  partially  to  pre- 
|*ent  overturning,  the  moment  of  stability  of  the  masonry 
is  neutralized.  As  the  water  is  of  less  weight  than  the 
masonry,  the  resultant  stability  is  greatly  diminished.  If 
Ithe  slope  of  the  upstream  face  were  made  45  deg.,  the 
'resultant  pressure  of  the  water  would  fall  at  the  edge  of 
ithe  middle  third.  Such  a  dam,  thoroughly  underdrained, 
388 


would  not  need  to  depend  upon  the  weight  of  the  masonry 
for  its  stability.  If  the  amount  of  masonry  can  be  reduced 
by  arching  and  the  use  of  buttresses  or  counterforts,  an 
economic  dam  may  result.  In  case  reinforced  concrete 
slabs  are  used  the  reinforcing  should  be  with  round  rods 
with  nuts  and  washers  on  the  ends  and  spliced  with  sleeve 
nuts,  so  as  to  reduce  to  a  minimum  dependence  upon  ad- 
hesion or  bond.  A  good  form  of  reinforcement  is  a  com- 
bination of  round  rods  and  angles  with  holes  punched  in 
them  to  receive  the  rods  and  act  as  bearing  plates  or 
washers.  Rods  should  have  two  nuts,  one  to  bear  against 
each  side  of  the  metal.  Rods  should  also  be  used  trans- 
verse with  the  main  rods  of  the  slabs,  so  as  to  tie  the  con- 
crete together  in  every  direction.  At  the  counterforts  or 
walls  supporting  the  slabs  there  should  be  angles  through 
which  the  rods  pass  and  to  which  also  rods  reinforcing 
the  counterforts  may  connect.  This  tying  together  of  the 
entire  structure  adds  greatly  to  its  stability  and  safetj 
and  lessens  the  probability  of  extended  failure,  if  a  loca. 
weakness  develops.  The  deep  slabs  that  would  be  requirec 
in  large  dams  should  have  a  set  of  rods  near  the  tensior 
side  of  slab  similar  to  the  horizontal  rods  in  beams  anc 
a  set  of  rods  that  curve  up  about  at  the  quarter  points 
these  are  to  take  the  shear  and  the  continuous  beam  stresse* 
of  the  slab.  All  of  these  rods  should  pass  through  angles 
The  entire  system  of  steel  reinforcement  should  be  a; 
rigidly  braced  and  held  in  place  as  possible  before  con 
crete  is  placed,  so  that  the  placing  of  concrete  will  no 
displace  the  parts. 

The  reason  that  adhesion  or  bond  should  not  be  reliec 
upon  in  a  reinforced  concrete  dam  is  because  water  unde: 
pressure  lessens  the  gripping  power  of  the  concrete. 

A  reinforced  concrete  dam  could  be  made  with  a  vertica 
slab  against  the  water  sustained  by  counterforts  or  but 
tresses  on  the  down  stream  side. 

A  dam  must  be  stable  against  sliding  on  its  foundation 
If  the  foundation  of  the  dam  is  in  rock,  notches  should  b 
cut  in  the  rock  so  that  slipping  will  be  prevented  by  th 
rock  itself.  In  general  dependence  should  not  be  place* 

389 


;  ipon  a  wall  of  earth  to  prevent  slipping  or  a  notch  in  an 
!  :arth  foundation  because  of  the  compressibility  of  earth. 
j  \ssuming  a  coefficient  of  sliding  friction  of  the  masonry 
>n  the  earth  of  l/2,  the  dam  would  be  stable  against  sliding 
f  its  weight  were  twice  the  horizontal  pressure  of  the 
vater.  Using  the  same  unit  weights  as  before,  it  will  be 
;een  by  a  simple  calculation  that  a  rectangular  dam  whose 
veight  is  twice  the  horizontal  pressure  of  the  water  would 
lave  a  width  of  .42  times  its  height.  A  triangular  dam 
vould  have  a  width  or  base  .83  times  its  altitude.  If  water 
vorks  its  way  under  the  dam,  it  will  lubricate  the  surface 
ipon  which  sliding  takes  place.  The  sliding  out  of  large 
:hunks  of  masonry  in  dams  that  have  failed  would  indicate 
hat  this  is  a  mode  of  failure  to  be  looked  for  and  guarded 
igainst.  That  such  a  failure  may  not  take  place  locally  it 
s  important  that  dams  be  made  of  monolithic  concrete 
md  not  of  blocks  of  stone.  It  is  also  important  that  some 
;teel  reinforcement  be  used,  even  in  solid  dams,  to  tie 
ihe  concrete  together.  Where  in  the  foundation  of  a  dam 
the  principal  bearing  surfaces  against  the  earth  are  made 
normal  to  the  resultant  pressure,  sliding  is  practically  elim- 
inated, and  settling  would  cause  a  uniform  movement  of 
the  dam  of  a  nature  similar  to  the  vertical  settlement  of 
|i  structure.  These  foundations  must  be  deep  enough  not 
o  cause  upheaval  of  the  earth  due  to  the  lateral  pressure. 
In  a  dam  with  counterforts  or  buttresses  inclined  shafts 
j:ould  be  made  use  of  as  foundations  for  the  counterforts 
||>r  buttresses  to  take  the  inclined  resultant  of  the  pressures 
(Being  separated  from  the  curtain  wall  in  contact  with  the 
water  these  would  not  be  subject  to  the  buoyancy  or  the 
rubricating  action  of  the  water  under  high  pressure. 
i  Anchor  bolts  in  the  natural  rock  to  tie  a  dam  down 
ikgainst  uplift  should  be  used  with  caution.  A  bolt  dropped 
m  a  drilled  hole  and  grouted  is  not  the  best  kind  of  anchor. 
|'f  steel  bolts  are  to  be  used  as  anchors,  it  is  better  to  ex- 
r:avate  expanding  holes  in  the  rock  and  fill  these  with  con- 
crete around  bolts  suspended  in  them. 
|  Arched  dams  are  sometimes  made,  which  have  their 
ibutments  in  the  rock  on  each  bank  of  the  stream.  Such 
390 


dams  are,  of  course,  convex  on  the  upstream  side.  The 
water  acts  as  a  horizontal  load  on  the  arch.  The  curve 
of  the  dam  in  any  horizontal  section  should  be  the  arc  of 
a  circle,  as  this  is  the  shape  of  a  curve  of  equilibrium  for 
a  uniform  load  normal  to  the  extrados  of  an  arch.  The 
pressure  around  the  arch  at  any  given  depth  h  is  62.5  hR 
per  foot  in  the  height  of  dam,  where  h  =  depth  below  sur- 
face of  water  and  R  —  radius  of  arch  in  feet.  The  arch 
could  not  be  a  true  reinforced  concrete  arch,  because  the 
load  is  a  constant  one,  and  there  is  no  bending  moment 
to  resist.  It  should,  however,  be  tied  together  with  rods 
runing  horizontal  and  vertical  to  prevent  the  concrete  from 
cracking.  The  unit  compression  on  the  concrete  (which 
should  be  1:2:4  concrete  of  Portland  cement  and  good 
sand  and  stone)  should  not  exceed  200  or  300  Ib.  per  sq. 
in.,  because  the  concrete  is  in  compression  over  the  entire 
surface,  and  there  is  no  reinforcement  against  diagonal 
shear.  Steel  should  not  be  counted  upon  to  take  any  of 
the  compression  of  the  arch. 


391 


The  Design  of  Reinforced  Concrete 
Chimneys. 

There  are  several  problems  that  enter  into  the  design 
of  reinforced  concrete  chimneys,  which  are  not  usually 
found  in  text  books  on  mechanics  of  materials.  These 
will  be  taken  up  as  a  preface  to  this  article. 

One  of  these  problems  concerns  the  position  of  the  line 
of  pressure  on  a  hollow  rectangular  column  of  elastic  ma- 
terial in  order  to  produce  only  compression  on  the  material. 
The  rectangular  column  will  be  taken  as  one  having  out- 
side dimensions  b  and  d  and  inside  dimensions  bf  and  d'. 
A  central  load  P  on  such  a  column  will  produce  a  unit 
compression  K  as  per  the  following  equation: 
K  =  P  +  (bd  —  b'd')  (i) 

If  the  load  P  be  shifted  a  distance  x  in  a  direction  par- 
allel to  the  side  d,  remaining  central  in  the  rectangle  in 
the  other  direction,  it  will  produce  bending  in  the  column 
in  addition  to  the  direct  stress.  The  eccentric  load  P  may 
be  considered  as  replaced  by  a  central  load  P  and  a  couple 
-each  of  whose  forces  is  P,  one  being  located  at  the  shifted 
position  of  the  load  P  and  the  other  being  at  the  center 
of  the  column  but  opposite  in  direction  from  the  other 
central  load,  thus  neutralizing  it.  The  effect  on  the  column 
is  then  a  couple  which  will  produce  a  bending  moment  Px 
and  a  direct  central  load  P.  The  moment  will  give  ten- 
*sion  along  one  edge  of  the  rectangle  and  compression  along 
the  other  edge  with  uniform  variation  between.  The  sec- 
tion modulus  of  the  hollow  rectangle  is  (bd3  —  b'd'3)-z-6d. 
.^Hence  the  extreme  fiber  stress  K'  due  to  the  moment 
Px  is 

K'=(6  Pxd)  +  (bd*  —  b'd's)         (2) 

When  K  =  Kf,  there  will  be  a  condition  of  no  stress  at 
one  edge  of  the  rectangle  and  an  extreme  fiber  stress  at 
the  opposite  edge  equal  in  intensity  to  double  the  unit 
compression  due  to  the  direct  load  P. 

For  any  given  rectangle  the  value  of  x  may  be  found 
by  equating  K  and  K'  of  equations  (i)  and  (2)  respec- 
tively and  solving.  This  value  of  x  will  give  the  position 

392 


4 

$ 

X  — 

5 

4 
y—  ! 

i 

X        H 
5" 

if 

•  y  "^ 

1 

.  5-0", 

i 

j 

f* 

i 

5--—^ 
7-'6" 

^*       o 

»4"           V 

2  I 

m 

_._z 

J 

T — r 

•FIG.  3. 


I5-O* 


393 


of  a  load  that  will  give  the  condition  named  in  the  last 

paragraph.     A  load  placed  anywhere  within  a  distance  x 

\  from  the  center  of  column  will  produce  only  compression 

\  in  the  column.     In  a  hollow  square  column  or  chimney 

i  whose  external  and  internal  diameters  are  d  and  d'  re- 

spectively we  find 

x=(d*  +  d'*)-r-6d        (3) 

The  resultant  pressure  on  the  section  of  a  hollow 
i  square  chimney  should  then  fall  within  this  distance  x  of 
i  the  center. 

When  d'  =  o,  that  is,  when  the  section  of  the  column 

'is  rectangular,  x  is  one-sixth  of  d.     This  is  the  familiar 

"proposition  that  the  center  of  pressure  in  a  rectangle  must 

\  fall  within  the  middle  third  of  the  base  in  order  not  to 

produce    tension    on    the    extreme    fiber.      When    d'  —  dt 

x  =  1/3  d,  showing  that  when  the  thickness  of  the  shell  is 

•small  compared  with  the  diameter  the  resultant  may  ap- 

iproach  a  point  one-third  of  the  diameter  from  the  center 

i  without  producing  tension  on  any  part  of  the  shaft. 

1     In  a  hollow  circle  whose  external  and  internal  diameters 

are  D  and  D'  respectively,  we  find  by  a  similar  operation 

-+          «> 


When  D'  =  o,  x=y%D,  which  shows  that  the  center  of 

pressure  must  fall  within  the  middle  quarter  of  the  diam- 

eter of  a  solid  circular  shaft  in  order  not  to  produce  ten- 

sion on  the  extreme  fiber.     When  Df  approaches  equality 

with  D,  x  approaches  *4  of  D,  showing  that  in  a  thin  shell 

the  resultant  may  fall  within  y±  of  the  diameter  from  the 

center  without  producing  tension  on  any  part  of  the  section. 

Another  problem  that  has  a  bearing  on  the  design  of 

chimneys  is  that  by  which  the  stress  may  be  found  in  a 

system  of   rods  disposed   in   a  circle   when   subject  to  a 

bending  moment  acting  on  the  circle.    This  will  be  solved 

!  through  the  medium  of  a  thin  tube  in  bending,  which  is 

I  still  another  problem  useful  in  the  solution  of  stresses  in 

i  chimneys.     The  moment  of  inertia  of  a  tube  or  circular 

|  shell  whose  thickness  is  t,  and  radius  R,  both  in  inches,  is 

394 


TT  /?*  t,  and  the  section  modulus  is  therefore  -TT  R*  t.  If 
we  let  K=  extreme  fiber  stress  on  the  tube  in  pounds 
per  square  inch  and  M  the  moment  on  the  same  in  inch- 
pounds,  we  have 

M  =  K*R*t     (5) 

(M  may  be  in  ft.-lbs.,  K  in  pounds  per  square  foot,  and 
R  and  t  in  feet.) 

Suppose  now  that  the  tubular  shell  is  replaced  with  a 
system  of  rods  equally  spaced  and  disposed  in  a  circle.  Let 
n  =  number  of  rods.  Then  2  TT  R-r-n  is  the  space  from 
rod  to  rod.  The  rod  that  is  located  at  the  point  of  max- 
imum extreme  fiber  stress  can  be  considered  as  taking  the 
stress  that  would  come  on  the  shell  in  an  area  equal  to 
the  spacing  of  rods  by  thickness  of  shell,  or  2  ?r  R  t-r-n. 
The  stress  on  this  rod  is  then  2  w  R  K  t-^-n.  Substitut- 
ing the  value  of  K  out  of  equation  (5)  in  this  we  have 
for  the  stress  5"  on  the  rod  receiving  the  maximum  stress 
S  =  2M  +  Rn  (6) 

Equation  (6)  is  remarkable.  It  is  derived,  as  observed, 
only  to  be  a  close  approximation  for  a  comparatively  large 
number  of  rods  arranged  in  a  circle.  By  trial  it  will  be 
found  to  be  exactly  true  for  12  rods,  8  rods,  6  rods,  4 
rods,  and  probably  for  any  even  number  of  rods  above 
these  numbers.  This  equation  could  be  used  in  finding  the 
maximum  pull  on  the  anchor  bolts  of  a  steel  stack.  It 
could  be  used  in  finding  the  stress  on  the  bolts  of  a  pipe 
coupling  under  bending.  It  could  be  used  in  finding  the 
stress  on  the  rivets  in  the  circular  seam  of  a  riveted  pipe 
under  bending,  as  in  the  case  where  the  pipe  spans  an 
opening. 

Another  problem  that  will  need  to  be  solved  concerns 
the  extreme  fiber  stress  on  a  hollow  circular  section  under 
bending.  The  formula  for  this  case  is 

M  =  .0982  (£>4  —  Z)'4)  K  ~  D  (7) 

The  calculations  on  a  reinforced  concrete  chimney  or 
stack  involve  the  determination  of  the  compression  on  the 
concrete  or  the  dimensions  necessary  to  keep  that  compres- 
sion within  certain  limits,  the  embedded  steel  required  to 

395 


relieve  the  concrete  of  all  tension,  and  the  base  necessary 
to  give  the  required  stability  against  the  wind. 

In  the  stack  shown  in  Fig.  2  it  is  desired  to  investigate 
the  stability  and  to  determine  the  amount  of  steel  neces- 
sary  to   reinforce   the   concrete.     The   areas   and   weights 
are  found  to  be  as  follows: 
Area  upper  section,  829  sq.  in.  =  5.76  sq.  ft. 
Area  middle  section,  1021  sq.  in.  —  7.09  sq.  ft. 
Area  outer  shell,  lower  section,  1583  sq.  in.  =  n.oo  sq.  ft. 
Area  inner  shell,  lower  section,  1021  sq.  in.  =  7.09  sq.  ft. 
Weights  at  150  Ib.  per  cu.  ft. : 

Upper    section    25,900 

Middle  section    31,900 

Outer  shell,  lower  section   66,000 

Inner  shell,  lower  section   42,500 

Plinth,  base  33, 700 

Frustum,   base    78,800 

Total  weight  of  stack   278,800 

The  moment  of  stability  of  the  stack  is  278,800  times 
one-sixth  of  the  width  of  the  base,  or  697,000  ft.-lb.  (The 
added  weight  due  to  the  thickening  up  at  section  Y  Y  is 
omitted  here  to  simplify  the  calculations.) 

The  wind  loads  (at  40  Ib.  per  sq.  ft.  on  one-half  the 
projection  of  the  cylinder)  are  as  follows: 

Upper  section,  40  X  ^  X  5.83  X  3O  =  3,5oo  Ib. 

Middle  section,  40  X  *A  X  5.83  X  30  =  3,500  Ib. 

Lower  section,  40  X  V*  X  7^  X  40  —  6,000.  Ib. 

The  load  on  the  upper  section  is  applied  85  ft.  above  the 
ground,  that  on  the  middle  section  is  applied  55  ft.  above 
the  ground,  and  that  on  the  lower  section  is  applied  20  ft. 
above  the  ground.  The  wind  moments  at  the  ground 
level  are 

3,500  X  85  =  297,500 
3,5oo  X  55  =  192,500 

6,000  X  20  =  120,000 


Total 610,000  ft.-lb. 

At  the  base  of  the  foundation  there  will  be  added  to  this 
396 


moment  13,000  X  5  =  65,000,  making  the  total  675,000  ft.-lb. 
This  is  less  than  the  moment  of  stability  previously  found. 
Hence  the  stack  is  stable  against  the  wind. 

The  area  of  the  base  is  225  sq.  ft.  Dividing  this  into 
the  total  weight  found  above  we  find  a  pressure  on  the 
soil  of  1,240  Ib.  per  sq.  ft.  When  the  wind  load  is  applied, 
the  pressure  on  the  soil  on  the  leeward  edge  is  almost 
double  this  amount.  (It  would  be  just  doubled  if  the 
overturning  moment  just  equaled  the  moment  of  stability.) 
A  pressure  of  2,400  Ib.  per  sq.  ft.  is  very  low  for  ordinary 
soil. 

At  the  section  XX  the  weight  of  the  stack  is  25,900  Ib. 
and  the  compression  due  to  dead  weight  is  31  Ib.  per  sq. 
in.  The  wind  moment  at  this  section  is  3,500  X  15  =  52,500 
ft.-lb.  The  concrete  is  able  to  resist  a  certain  part  of  this 
without  suffering  any  tension  on  the  extreme  fiber.  The 
distance  from  the  center  that  the  resultant  pressure  may 
fall  to  give  this  condition  of  no  tension  is  the  value  of  x 
in  equation  (4).  Solving  for  the  section  XX  we  find  x 
is  1.30  ft.  Hence  (taking  moments  about  a  point  x  feet 
from  the  center  of  stack)  the  moment  of  stability  of  the 
stack,  without  relying  upon  the  steel,  is  25,900  X  J-3O  — 
33,700  ft.-lb.  This  leaves  18,800  ft.-lb.  to  be  taken  by  the 
steel. 

At  section  Y  Y  the  wind  moment  is  3,500  X  45  +  3>5oo 
X  15  —  210,000  ft.-lb.  The  value  of  x  is  1.27  ft,  and  the 
moment  of  stability  of  the  concrete  is  57,800  X  1.27  =  73,400 
ft.-lb.  This  leaves  136,600  ft.-lb.  to  be  taken  by  the  steel. 

At  section  ZZ  the  wind  moment,  previously  found,  is 
610,000  ft.-lb.  The  value  of  x  is  1.64  ft.  and  the  moment 
of  stability  of  the  concrete  is  123,800  X  1-64  =  203,000  ft.-lb. 
This  leaves  407,000  ft.-lb.  to  be  taken  by  the  steel. 

For  the  steel  reinforcement  we  will  take  the  neutral 
axis  in  the  center  of  the  shaft  in  all  cases  and  allow  the 
concrete  to  take  whatever  compression  develops.  The 
critical  point  is  then  the  outermost  rod  on  the  tension  side. 
The  tension  on  this  rod  is  found  by  equation  (6).  Or 
assuming  a  size  of  rod  the  number  of  rods  required  may  be 
found  by  the  same  equation. 

397 


Assuming  that  ^j-in.  round  rods  will  be  used  vertically. 
12,500  Ib.  per  sq.  in.  the  permissible  tension  on  one  rod 

7,520  Ib.  Keeping  these  rods  3  in.  from  the  outer  sur- 
face of  the  stack,  the  radius  of  their  circle  is  3.5  ft.  Sub- 
stituting in  equation  (6)  we  have  7,520  =  2X407,000-7^ 
3.5  n,  from  which  w  =  3i  bars. 

At  section  Y  Y,  using  the  same  bars  and  2  ft.  9  in.  for 
the  radius,  we  have  7,520  =  2  X  136,600  -r-  2.75  n,  from 
which  n  =  13. 

If  32  bars  be  used  in  the  lower  section,  half  of  them 
may  be  dropped  at  section  Y  Y. 

At  section  X  X  but  little  steel  is  required.  There  should 
be  some  rods,  however,  to  prevent  the  cracking  of  the 
'concrete.  Eight  of  the  7/s-'m.  rods  could  be  continued  io 
the  top  of  chimney,  or  smaller  rods  could  be  used,  say  16 
half-inch  round  rods  lapping  those  of  the  section  below. 
Another  method  would  be  to  run  four  of  the  ^-in.  rods 
the  full  length  and  to  use  smaller  rods  between  these  to 
tie  the  concrete  together. 

The  %-in.  rods  should  have  anchorage  in  the  founda- 
tion; preferably  by  a  circular  angle  punched  to  receive 
them,  or  by  anchor  plates.  Two  nuts  on  the  end  of  each 
rod  would  insure  a  bearing  on  the  metal.  Where  rods 
join,  they  should  be  threaded  and  have  sleeve-nut  splices. 

In  the  horizontal  direction  rods  in  circles  should  be 
placed  about  every  20  or  30  in.,  their  ends  being  lapped 
a  foot  or  more.  These  rods  could  be  l/2  in.  square.  They 
should  be  wired  to  the  vertical  rods. 

Around  openings  in  the  side  additional  rods  are  needed 
for  reinforcement,  also  possibly  a  thickening  of  the  con- 
crete. 

Where  the  diameter  of  the  outer  shell  changes  there  is 
a  weak  section.  The  bend  in  the  rods  induces  horizontal 
thrust,  and  there  is  shear  on  the  concrete  because  of  the 
change  in  direction  of  the  line  of  pressure.  It  is  recom- 
mended that  the  bends  in  rods  be  made  in  the  thickened 
portion  of  the  shell  and  that  curved  angles  be  used  at 
these  bends  to  stiffen  the  concrete,  as  shown  in  Fig.  4. 

The  inner  shell  needs  rods  both  vertically  and  horizontally 


to  keep  the  concrete  from  cracking.  This  inner  shell  is 
kept  separate  from  the  outer  shell,  except  near  the  bottom, 
where  the  air  space  is  sometimes  filled  in.  The  purpose 
is  to  allow  free  expansion  and  contraction  of  the  highly 
heated  part.  The  amount  of  steel  used  to  reinforce  con- 
crete where  there  is  no  calculable  stress  is  usually  made 
from  1-500  to  i-iooo  of  the  area  of  concrete. 

The  compressive  stress  on  the  concrete  is  another  matter 
for  investigation.  Z  Z  is  the  critical  section;  other  sec- 
tions will  be  found  to  have  considerable  less  unit  stress. 
The  compression  from  dead  load  is  78  Ib.  per  sq.  in.  By 
equation  (7),  using  610,000  for  M,  we  find  an  extreme 
fiber  stress  of  33,800  Ib.  per  sq.  ft.  or  235  Ib.  per  sq.  in. 
This  makes  the  maximum  compression  at  this  section  313 
Ib.  per  sq.  in.,  which  is  about  right.  Concrete  in  such 
case  should  not  be  subject  to  the  usual  allowable  compres- 
sive unit  of  500  Ib.,  because  it  is  not  confined  on  one  side, 
as  in  the  case  of  beams  and  slabs.  This  concrete  is  more 
in  the  nature  of  a  column.  The  hoop  reinforcement  does 
not  have  the  efficiency  in  this  case  that  it  has  in  a  hooped 
column.  As  a  check  on  the  compressive  stress  on  the  con- 
crete we  may  use  the  same  moment  in  equation  (5)  and 
the  mean  value  of  R,  or  3.5.  The  result  is  220  Ib.  per 
sq.  in.  as  compared  with  235  Ib.  found  by  the  more  exact 
method. 

The  design  of  the  chimney  would  be  simplified  and  im- 
proved, from  a  structural  standpoint,  if  the  offset  in  the 
outer  shell  could  be  avoided. 

For  the  outer  shell  of  this  chimney  the  concfete  used 
should  be  a  i  :2 14  mixture  with  small  sized  broken  stone 
of  good  quality.  The  inner  shell  should  be  a  concrete  that 
will  resist  a  moderately  high  heat.  No  limestone  should 
be  used  in  this  part.  Small  gravel  and  sand  or  trap  and 
sand  would  be  suitable. 

If  sand  alone  is  used  with  the  cement  such  mixtures  as 

i  :7  or  8  should  not  be  employed.    The  voids  in  sand  are 

too  great  to  be  filled  with  this  small  proportion  of  cement. 

About  4  or  5  parts  of  sand  to  one  of  cement  ought  to  be 

399 


the  limiting  ratio,  and  even  this  ratio  should  only  be  used 
with  a  very  coarse  sand. 

The  spread  of  the  footing  of  this  chimney  is  not  enough 
to  require  much  if  any  reinforcement  in  the  concrete.  It 
would,  however,  be  desirable  to  have  some  rods  laid  par- 
allel to  each  side  and  some  laid  diagonally  in  both  di- 
rections. 


j      T 

'     vfno 


f 


>  ariT) 


y^o!  ? 


The  Design  of  Domes,  Vaults  and 
Conical  Coverings. 

While  the  stresses  in  a  flat  plate  supported  on  all  sides, 
or  a  flat  slab  similarly  supported,  are  more  or  less  in- 
definite, after  deflection  takes  place,  because  of  the  fact 
that  a  flat  plate  may  actually  act  as  a  portion  of  a  spherical 
shell  of  very  long  radius,  the  stresses  in  a  dome  or  conical 
roof  are  capable  of  more  exact  determination.  Also  the 
analysis  of  these  stresses  is  comparatively  simple. 

The  stresses  in  a  conical  covering  or  roof,  such  as  that 
on  a  circular  tank  will  first  be  considered.  Given  a  conical 
covering  such  as  that  shown  in  Fig.  I.  Let  the  weight 
above  the  line  AB  be  represented  by  IV.  This  can  be  re- 
solved into  two  components,  namely  H  and  T.  A  thin 
cone  not  capable  of  taking  any  bending  but  only  com- 
pression and  tension  may  resist  both  of  these  forces  or  sets 
of  forces.  (The  cone  is  somewhat  analogous  to  a  thin 
tube  under  external  pressure  so  that  if  the  thickness  is 
relatively  small  it  may  be  in  a  state  of  unstable  equi- 
librium.) The  component  T  will  give  compression  in  the 
direction  of  an  element  of  the  cone,  and  the  component 
H,  being  continuous  around  a  circle  whose  radius  is  r, 
acts  like  external  pressure  on  a  cylinder,  producing  com- 
pression also. 

The  total  amount  of  T  is  found  by  the  equation 

T=Wmr_  (1) 

ft 

The  area  upon  which  this  force  acts  is  a  ring  whose 
radius  is  r  and  whose  thickness  is  t  or  an  area  2     TT  r  t . 
Dividing  this  into  the  above  value  of  T  we  have  for  a  unit; 
compression  C  in  the  direction  of  an  element  of  the  cone 
r         Wm 

C=-2^T~  <2> 

The  weight  W  will  include  the  dead  weight  of  the  part 

of  the  cone  above  the  line  AB,  including  any  structural 

features  outside  of  the  cone  itself,  also  any  snow  load  or 

live  load  that  may  come  upon  that  part  of  the  cone. 

401 


The  force  H  in  Fig.  i  is  resisted  by  hoop  compression 
in  horizontal  planes.  The  force  T  is  cumulative  and 
reaches  the  value  in  equation  (i)  only  at  the  foot  of  the 
slope  mr.  The  force  H  is  resisted  by  rings  or  hoops  of 
stress  distributed  along  the  entire  surface  of  the  cone, 
that  is;  these  rings  make  up  the  cone.  In  order  to  arrive 
at  the  amount  of  this  hoop  compression  we  observe  that 
each  ring  is  in  effect  an  element  of  a  cylinder  under  ex- 
ternal pressure.  It  is  well  known  that  the  tension  or  com- 
pression on  the  shell  of  a  cylinder  due  to  a  radial  pres- 
sure, outward  or  inward,  of  any  given  intensity  is  equal 
to  the  amount  of  that  pressure  on  a  radius.  In  other 
words  the  tension,  or  compression  on  the  ring  or  hoop  is 
equal  to  the  total  pressure  around  the  circumference  di- 
vided by  2  TT  .  Therefore  H  divided  by  2  -  is  equal  to  the 
stress  on  an  element  mr  of  the  cone.  But  H  =—  Wr  -f-  h, 
and  the  total  compression  along  the  element  mr  is 

*-s- 

This  compression  is  not  uniformly  distributed  along  the 
element,  but  varies  in  intensity.  In  order  to  find  the  value 
of  K,  for  the  case  where  the  weight  is  only  that  of  the 
cone  itself,  we  will  substitute  for  W  the  weight  of  the 
cone  above  the  section  AB,  or  w  m  n  r*  t,  where 
w  =  weight  per  cu.  ft.  of  the  material  of  the  shell  other 
dimensions  being  in  feet.  Then 

K=-^fL  (4) 

The  unit  compression  at  any  section  is  found  by  sub- 
stituting in  (3)  an  element  of  the  weight  of  the  cone  and 
dividing  by  an  element  of  the  area.  Letting  P  represent 
this  unit  compression  we  find 


(5) 

If  in  equation  (2)  we  substitute  for  W  the  weight  of  a 
conical  shell  whose  radius  is  r,  or  TT  f9  m  w  t>  we  shall 
have 

(6) 

402 


Fig-  -I. 


a     V 


- 

2TT 


(b)       5n 


403 


We  see  from  equations  (5)  and  (6)  that  the  thickness 
of  the  conical  shell  does  not  enter  in  the  determination 
of  the  unit  stress  in  a  cone  supporting  its  own  weight  only 
(in  a  shell  where  the  volume  is  sensibly  equal  to  the  area 
of  the  median  cone  by  the  thickness).  It  may  also  be 
shown  by  equating  C  and  P  in  equations  (5)  and  (6) 
that  when  m  equals  the  square  root  of  2,  the  intensity 
of  stress  in  both  directions  is  the  same.  This  is  true 
when  the  angle  of  the  element  of  the  cone  with  the  hori- 
zontal is  45  deg. 

The  thickness  of  concrete  in  the  cone  is  determined 
by  other  considerations  than  the  weight  of  the  shell  itself. 
A  uniform  load,  such  as  a  snow  load  uniformly  distributed 
would  not  add  much  stress.  The  weight  of  a  man  on  the 
roof  of  a  tank  or  snow  load  on  one-half  only  are  possi- 
bilities that  must  be  considered.  These  scarcely  admit 
of  calculation.  Hence  a  simple  cone  without  ribs  would  be 
designed  largely  by  judgment.  A  thickness  of  shell  of  4  in. 
for  a  tank  15  ft.  in  diameter  and  6  in.  for  a  tank  25  ft.  in 
diameter  would  probably  meet  the  requirements.  Steel 
rods  in  circles  around  the  cone  and  rods  down  the  slope 
would  be  valuable  to  insure  the  integrity  of  the  roof  and 
to  guard  against  shrinkage  cracks.  If  any  man  holes  are 
to  be  left  in  the  roof,  the  concrete  around  the  openings 
should  be  reinforced  with  steel  rods.  The  circular  and 
sloping  rods  in  the  conical  covering  are  not  true  reinforc- 
ing rods,  because  they  would  not  take  tension.  There  is 
no  basis  for  finding  their  size  for  the  same  reason. 

At  the  foot  of  the  slope,  if  the  cone  is  supported  on  ver- 
i  tical  walls,  there  is  a  tension  which  is  equal  to  the  total 
compression  exerted  on  a  vertical  section  from  the  apex 
to  the  foot  of  the  slope,  that  is,  the  sum  of  all  of  the 
hoop  compression  in  the  horizontal  rings.  The  amount  of 
this  is  found  by  equation  (3)  by  substituting  R  for  r.  For 
example,  given  a  tank  15  ft.  in  diameter,  with  m  =  1^4, 
the  concrete  being  4  in.  thick,  and  h  =  5.63  ft.  The  weight 
of  the  concrete  in  the  conical  roof  is  11,000  Ibs.,  at  150 
Ibs.  per  cu.  ft.  A  snow  load  at  30  Ibs.  per  horizontal 
square  foot  would  weigh  5,300  Ibs.  Using  16,300  for  W 
404 


in  eq.  (3)  we  find  K  =3,5oo  Ibs.  At  10,000  Ibs.  per  sq.  in. 
this  would  require  a  jj-in.  round  rod.  This  rod  should 
be  directly  over  the  wall  of  the  tank.  The  ends  should 
be  joined  by  a  turnbuckle  or  else  lapped  50  diameters  or 
more. 

A  conical  bottom  in  a  tank  has  the  stresses  reversed 
from  those  of  a  roof,  and  on  account  of  the  fact  that 
a  liquid  exerts  normal  pressure  against  the  bottom  there 
will  be  additional  stresses  in  the  rings.  Equation  (i) 
will  serve  to  determine  the  stress  down  the  slope,  which 
will  be  tension  instead  of  compression.  W  is  to  be  taken 
as  the  weight  of  the  cone,  the  radius  of  whose  base  is  r, 
plus  the  weight  of  the  liquid  directly  over  it.  The  great- 
est amount  of  steel  is  needed  near  the  junction  of  bottom 
and  sides.  There  should  be  an  angle  at  this  junction  bent 
into  a  ring  and  punched  to  receive  the  rods.  The  rods 
should  be  round  and  should  have  thread  and  nut  on  the 
end  to  anchor  to  this  angle.  It  is  best  to  make  all  rods 
of  the  same  diameter.  Equation  (i)  may  be  solved  for 
r=i  ft,  2  ft.,  3  ft,  etc.  Find  where  the  value  of  T  is 
one-half  the  maximum,  and  let  half  of  the  rods  run  50 
times  their  diameter  beyond  this,  the  others  to  continue 
down  the  slope:  half  of  these  may  end  50  diameters  be- 
yond the  point  where  the  stress  is  again  half  as  great,  etc. 
Some  rods  should  run  to  the  apex  of  the  cone  and  anchor 
to  a  small  circular  angle.  For  the  ring  stresses  solve 
equation  (5)  for  the  unit  tension  on  the  concrete  at  any 
point,  due  to  the  weight  of  the  bottom.  For  the  liquid 
pressure 

9_D 


Where  P"  =  unit  tension  on  concrete,  D  =  depth  of  liquid 
over  the  section  under  consideration,  w'  =  weight  per  cu. 
ft.  of  liquid.  The  sum  of  these  two  unit  tensions  is  to  be 
converted  into  tension  in  steel  rods  according  to  the  spac- 
ing of  rods  assumed. 

At  the  junction  of  the  shell,  or  side  of  tank,  and  the 
conical  bottom  there  will  be  a  compression,  in  amount 
equal  to  the  value  of  K  in  equation  (3),  when  W  —  total 
405 


weight  of  bottom  of  tank  and  liquid  contents.  This  must 
be  resisted  by  concrete,  and  there  should  be  area  enough 
of  concrete  close  to  this  corner  to  take  the  compression 
at  about  200  Ibs.  per  sq.  in.  It  is  of  course  uncertain 
just  how  much  of  the  walls  and  bottom  may  be  included 
in  the  ring  at  the  junction  to  take  this  compression.  A 
fair  proportion  would  include  twice  the  thickness  of  wall 
up  the  side  and  twice  the  thickness  of  bottom  down  the 
slope.  Then  the  concrete  over  the  supporting  wall  should 
be  thickened  as  shown  in  Fig.  I. 

A  dome  may  be  analyzed  in  a  manner  somewhat  sim- 
ilar to  a  conical  covering.  In  the  dome,  as  in  the  conical 
roof,  a  thin  shell  will  support  uniform  load  by  tensile  and 
compressive  stresses  alone,  though  if  the  thickness  is  rel- 
atively small  the  equilibrium  will  be  unstable. 

If  the  dome  is  segmental,  as  at  (a)  Fig.  2,  and  parabolic 
in  section,  a  portion  having  a  base  whose  radius  is  r  will 
have  stresses  at  the  foot  of  the  slope  (in  the  direction  of  the 
slope)  corresponding  to  those  in  a  cone  whose  altitude  is 
h,  the  cone  being  tangent  to  the  dome.  Because  of  the 
fact  that  it  is  a  property  of  a  parabola  the  altitude  of  the 
cone  will  be  twice  that  of  the  dome,  as  indicated.  It  is  to 
be  remembered  that  n  is  not  a  constant  in  this 
case,  as  in  the  case  of  the  cone.  For  the 
weight  of  the  dome  itself  the  superficial  area  is  very 
close  to  the  area  of  a  circle  whose  radius  is  the  chord 
m'r.  (The  area  of  a  segment  of  a  spherical  sur- 
face is  exactly  equal  to  the  area  of  a  circle  whose  radius 
is  this  chord  of  one-half  of  the  arc.)  The  volume  is  then 
equal  to  the  product  of  this  area  and  the  thickness  /.  For 
a  segmental  dome,  as  shown  at  (a),  reinforcement  is 
needed  over  the  supporting  wall  in  the  shape  of  a  steel 
hoop  to  take  the  thrust.  Assuming  a  dome  20  ft.  in  diam- 
eter and  5  in.  thick,  we  find  a  weight  of  22,800  Ibs.  and 
a  snow  load  of  9,400  Ibs.  If  the  dome  has  a  rise  of  4  ft. 
at  the  center,  h  =  S.  Substituting  in  eq.  (3)  we  find 
K  =  6400  Ibs.  At  10,000  Ibs.  per  sq.  in.  this  would  re- 
quire a  yf-in.  round  rod. 

The   circular  stresses    (at  other   sections   than  directly 
406 


over  the  wall)  in  a  segmental  dome  do  not  correspond  to 
those  in  a  tangent  cone.  But  as  these  do  not  play  a  very 
important  part  in  proportioning  a  dome,  unless  it  ap- 
proaches a  hemisphere,  they  will  be  taken  up  only  in  the 
case  of  the  hemispherical  dome. 

In  the  hemispherical  dome  such  as  shown  at  (6),  Fig. 
2,  the  tangential  thrust  Tf  at  any  section  is  found  by  the 
following 

T  —  W  cosec  x          (8) 

where  W  =  weight  of  dome  and  load  upon  the  same  above 
the  section  considered.  If  the  only  weight  supported  is 
that  of  a  dome  of  uniform  thickness  at  w  Ibs.  per  cu.  ft. 
we  may  find  W  thus  :  The  area  of  the  segment  of  a 
sphere  is  equal  to  the  circumference  of  a  great  circle  by 
the  altitude  of  the  segment.  The  weight  of  this  segment  is 
then  2  TT  R2  (i  —  cos#)  tw.  The  area  of  the  ring  tak- 
ing this  tangential  thrust  is  2  K  R  t  sin  x.  Using  the 
weight  just  found  for  W  in  equation  (8)  and  dividing  by 
the  area  just  found  we  find  for  a  unit  compression  C'  due 
to  thrust  T. 

C>=Rvl-cosx^<vv>  (9) 

sm*x        r2 

The  intensity  of  this  pressure  varies  from  R  w  just 
over  the  supporting  wall  to  one-half  as  much  as  the  top. 
Hence  a  dome  designed  to  take  a  uniform  unit  thrust, 
supporting  its  own  weight  only,  would  be  thinner  at  the 
crown  than  over  the  supporting  wall.  A  snow  load,  add- 
ing weight  near  the  crown  without  adding  to  the  capacity 
of  the  dome  to  support  the  weight,  would  tend  to  equalize 
the  stress. 

For  the  annular  or  ring  stresses  the  sum  of  these  from 
the  crown  down  to  the  end  of  radius  r  is 


27T 

Or  substituting  for  Wy  for  a  dome  of  uniform  thick- 
ness, the  weight  of  the  segment,  as  previously  found  we 
have 

K'  —  R2  t  w  (i—  cos  x)  cot  x         (n) 

407 


The  unit  intensity  of  this  hoop  compression  is  found  by 
differentiating  the  value  of  Kf  in  eq.  (n)  and  dividing 
by  R  t  dx,  which  is  the  differential  increment  to  the  area. 
The  result  is  a  unit  compression  P'  as  per  the  following 
equation. 

P'=Rw(cos  x— L "\  ( 12) 

V  cos  -r+1      ) 

By  examination  of  equation  (12)  it  will  be  seen  that 
for  x  =  o  the  intensity  of  stress  is  ^  R  w,  which  is  the 
same  as  that  of  the  thrust,  found  by  equation  (9),  at  the 
crown  of  dome.  As  this  is  positive  the  stress  is  com- 
pression. When  x  =  90  deg.,  P'  —  ( —  Rw),  which  is  also 
the  same  in  intensity  as  the  thrust  found  by  equation  (9), 
over  the  supporting  wall.  As  this  stress  is  negative  it  is 
tension.  When  cos  x  =  y*  (j/5 — i),  P'  —  o.  This  is 
true  when  x  =  51  deg.-49  min.  There  is  thus  a  point  where 
the  intensity  of  the  hoop  stress  is  zero.  Above  this  point 
the  hoop  stresses  are  compression  and  below  it  they  are 
tension.  Where  compressive  stresses  occur,  no  steel  rein- 
forcement would  be  demanded  for  these  stresses  alone. 
Where  tensile  stresses  occur,  steel  reinforcement  would  be 
required  in  a  concrete  dome.  The  tension  on  steel  rein- 
forcement would  be  found  by  solving  eq.  (12)  for  the 
unit  stress  at  any  point  and  multiplying  this  by  the  area 
of  concrete  surrounding  a  rod.  In  a  dome  30  ft.  in  diam- 
eter and  6  in.  thick  at  a  section  close  to  the  supporting 
wall  the  unit  stress  =  2tw  or  15  X  150  =  2,250  Ibs.  If  we 
assume  rods  one  foot  apart,  one  rod  would  be  surrounded 
by  ^2  sq.  ft.  of  concrete  and  have  a  stress  of  only  1,125  Ibs. 

There  is  no  thrust  to  take  at  the  springing  of  this  dome, 
as  in  the  cone  or  segmental  dome,  as  the  sides  start  vertn 
cal.  In  the  cone  and  segmental  dome  there  is  a  hoop  stress 
at  the  base  or  springing  which  just  balances  the  compres- 
sive hoop  stresses  along  the  vertical  section  through  the 
axis.  In  the  hemispherical  dome  this  equality  or  balanc- 
ing of  horizontal  forces  is  accomplished,  as  explained  under 
equation  (12),  by  positive  and  negative  hoop  stresses  along 
the  meridian. 

In    a    segmental    or    hemispherical    tank    bottom    the 
408 


stresses  for  the  weight  of  the  bottom  alone  will  be  equal 
in  intensity  to  those  found  for  the  dome  but  reversed  in 
sign.  The  unit  stress  in  the  direction  of  the  meridian  is 
found  by  the  following  equation. 

C^-l™  (13) 

where  Ci  =  unit  tension  at  point  S,  Fig.  2  at  (c),  w'  —  wt. 
per  cu.  ft.  of  liquid,  D'  —  average  depth  of  liquid  in 
MLSQN. 

The  unit  stress  in  horizontal  rings  may  be  found  by  the 
following  equation. 


P  _w'£{ 
'~— V 


(14) 


where  Pi  =  unit  tension  at  point  S,  and  D"  —  depth  of 
liquid  to  point  S. 

The  depth  D'  is  found  by  adding  to  the  altitude  of  the 
cylinder  MNSL  the  average  altitude  of  the  spherical 
segment  N  Q  S.  The  average  altitude  of  the  segment  of 
a  sphere  lies  between  2/3  and  ^2  of  the  altitude;  that  is, 
the  volume  will  lie  between  2/3  and  l/z  of  the  volume  of  a 
cylinder  of  the  same  base  and  altitude.  When  the  angle 
x  approaches  zero,  the  coefficient  is  one-half,  which  is  the 
exact  coefficient  for  a  paraboloid,  and  a  flat  circular  arc 
approaches  coincidence  with  a  parabola.  When  x  —  30  deg., 
the  coefficient  is  .512;  when  .ar  =r  45  deg.,  it  is  .529;  when 
x  =  60  deg.,  it  is  .556.  For  x  =  go  deg.,  or  when  the  seg- 
ment is  a  complete  hemisphere,  the  coefficient  is  2/3. 

To  reduce  tension  in  the  concrete,  as  found  by  equations 
(13)  and  (14)  to  tension  in  steel  reinforcing  rods,  multi- 
ply the  unit  values  there  found  by  the  assumed  spacing 
of  rods  times  the  thickness  of  concrete. 

In  a  ribbed  dome,  that  is  a  dome  supported  by  a  sys- 
tem of  arched  ribs  meeting  in  a  circle  or  regular  polygon 
at  the  top,  each  rib  is  like  the  half  of  an  arch.  Between 
the  ribs  the  covering  may  be  a  slab  of  reinforced  concrete. 
This  slab  would  be  designed  according  to  the  methods  of 
design  used  for  floor  slabs.  As  the  inclination  of  the  slab 
to  the  horizontal  increases,  the  possibility  of  carrying  a 
409 


snow  load  decreases,  and  the  effect  of  the  weight  of  the 
slab  itself  in  producing  bending  diminishes.  The  compo- 
nent of  the  dead  weight  that  produces  bending  in  the  slab 
is  the  weight  times  the  cosine  of  the  angle  made  with  the 
horizontal.  For  the  stress  in  the  rib  lay  a  rib  out  to  scale 
and  estimate  the  weight  carried  at  points  at  intervals 
along  its  length.  Take  moments  of  these  several  loads  and 
the  reaction  at  the  foot  of  rib  around  the  upper  end  of  the 
rib.  This  moment  divided  by  the  vertical  distance  from 
upper  end  to  foot  of  rib  will  give  the  horizontal  thrust. 
From  these  forces  construct  the  equilibrium  polygon.  (See 
similar  operation  and  construction  farther  on  in  the  case 
of  filter  vaults.)  This  equilibrium  polygon  will  give  the 
direct  stress  in  the  rib  and  will  give  the  bending  moment 
at  any  section.  For  the  latter,  where  the  equilibrium  poly- 
gon departs  from  the  center  line  of  the  rib,  the  bending 
moment  is  equal  to  the  product  of  the  force  in  the  poly- 
gon and  the  distance  from  the  center  of  the  rib  to  the 
force,  measured  perpendicular  to  the  force. 

A  form  of  vault  much  used  for  filter  covers  consists  of 
a  system  of  groined  arches  carried  by  square  posts  or 
piers,  spaced  equal  distances  in  both  directions.  These 
arches  spring  in  four  directions  from  the  piers.  At  the 
piers  the  arches  are  of  course  the  width  of  the  pier,  and 
at  this  section  they  are  thickened  vertically.  Midway 
between  the  piers  the  width  of  concrete  arch  is  equal  to  the 
distance  center  to  center  of  piers.  The  concrete  is  usually 
plain,  and  the  vaults  are  covered  with  three  feet  or  so  of 
earth.  Some  such  vaults  are  described  in  Engineering 
News,  November  8,  1906,  and  Engineering  Record,  May 
19,  December  15,  December  22,  1906,  April  27,  1907. 

The  load  to  be  carried  consists  principally  of  the  dead 
weight  Allowance  should  also  be  made  for  the  superim- 
posed load  of  teams  driving  over  the  ground.  In  this  in- 
vestigation only  the  dead  load  will  be  calculated.  The  live 
load  could  be  considered  as  a  uniform  load  of  100  or  200 
Ibs.  per  sq.  ft.,  since  the  deep  earth  fill  serves  to  distribute 
well  the  live  load. 

Fig.  3  shows  a  section  of  a  filter  vault  taken  through 
410 


F.q.3 


411 


a  pier  and  the  outside  wall  or  abutment.  This  illustrates 
<  the  various  points  to  be  considered,  namely,  the  pier,  the 
half  of  one  of  the  groined  arches,  the  half  arch  springing 
from  the  outer  wall,  and  the  outer  wall  or  abutment.  The 
distance  c.  to  c.  of  piers  is  15  ft.  The  span  of  arch  is  the 
distance  from  face  to  face  of  piers  or  from  face  of  pier 
to  inner  face  of  outer  wall;  this  is  13  ft.  2  in.  Half  of 
this  is  divided  into  10  equal  parts,  and  the  weights  of  con- 
crete and  earth  in  each  part  are  calculated.  These  weights 
are  shown  in  Fig.  3;  those  on  the  left  side  of  the  center 
are  for  the  half  of  a  groined  arch,  and  those  on  the  right 
side  are  for  the  half  barrel  arch. 

By  taking  moments  around  the  center  of  arch  at  crown, 
using  the  applied  loads  to  the  left  and  the  reaction  24,200 
Ibs.,  and  dividing  the  moment  thus  found  by  the  rise, 
i  ft.  nl/2  in.,  we  obtain  the  horizontal  thrust,  H,  or  48,500 
Ibs.  The  rise  of  the  arch  is  the  vertical  distance  from 
the  center  line  of  arch  ring  at  springing  (center  point  of 
line  QS)  and  the  center  of  arch  at  crown.  With  this 
thrust  H  and  the  several  vertical  loads  the  stress  diagram 
to  the  left  is  drawn.  By  drawing  lines  parallel  to  these 
rays  the  equilibrium  polygon  beginning  at  R  is  constructed 
for  the  left  half.  By  calculating  the  horizontal  thrust 
from  the  bending  moment  at  center  of  arch  it  is  assured 
that  the  equilibrium  polygon  will  pass  through  the  center 
line  of  the  arch  ring  at  the  crown.  It  is  seen  that  this 
polygon  lies  within  the  middle  third  of  the  arch  ring 
throughout.  Hence  the  arch  will  be  stable,  if  the  unit 
stress  is  not  too  great. 

The  thrust  for  the  half  arch  to  the  right  must  be  the 
.same  as  that  to  the  left,  but,  as  the  load  is  more,  the  rise 
must  be  greater.  The  rise  in  this  case  was  found  by  first 
laying  out  a  trial  arch  and  estimating  the  weight  and 
finding  the  moment.  Dividing  this  moment  by  the  known 
thrust  gave  the  rise  to  agree  with  the  calculated  loads. 
By  another  trial  a  rise  and  moment  were  found  that  agreed 
with  the  thrust.  The  equilibrium  polygon  for  this  half 
arch  is  found  as  for  the  other.  It  also  falls  inside  of  the 
middle  third  of  the  arch.  In  all  cases  the  curves  for  top 
412 


and  bottom  of  the  arches  were  made  arcs  of  circles.    It  will 
be  seen  that  the  equilibrium  polygons  almost  coincide  with! 
arcs  of  circles.    The  unit  compression  on  the  arch  is  seenp 
to  be  only  about  100  Ibs.  per  sq.  in. 

The  thrust  of  the  several  arches  against  the  piers  must 
balance.    No  part  can  be  taken  by  the  piers.    If  the  arches  I 
are  not  loaded  alike,  the  additional  thrust  must  be  absorbed  1 
in  the   arches   themselves.     For   this   there   is   a   surplus! 
strength   imparted  by  the  horizontal   stiffness.     The   pier  I 
will  then  be  in  simple  compression.    The  load  is  about  100,- 
ooo  Ibs.,  and,  as  the  area  is  484  sq.  in.,  the  unit  compression 
is  a  little  more  than  200  Ibs.  per  sq.  in.    This  is  not  exces- 
sive for  a  pier  of  this  length,  not  reinforced,  if  made  of  I 
good  1:2:4  concrete,  when  the  pier  is  not  subject  to  any 
side  forces.     If  live  load  is  to  be  provided  for,  however, 
the  pier  should  be  made  larger,  so  that  there  will  be  no 
more  than  about  200  Ibs.  per  sq.  in.  in  compression. 

On  the  wall  the  forces  are  the  72,000  Ibs.  due  to  the 
arch,  acting  on  15  ft.  of  wall,  the  weight  of  15  ft.  of 
ABDEFG  in  concrete,  and  the  weight  of  15  ft.  of  JGFLK 
in  earth.  The  moments  of  these  should  balance  about  Ct 
which  is  1-3  of  AB  from  B.  If  the  moment  of  the  con- 
crete and  earth  is  not  sufficient  to  balance  that  of  the 
72,000  Ibs.,  the  wall  should  be  made  wider  at  the  base. 
Wifh  the  dimensions  shown  the  moments  were  found  to 
balance  about  C.  Only  the  part  of  the  earth  load  to  the 
left  of  CK  is  taken,  because  that  to  the  right  does  not' 
increase  the  stability  of  the  wall  (considering  its  weight 
alone).  It  cannot  be  said  to  decrease  the  stability,  hence 
it  is  neglected.  If  water  is  in  the  filter,  not  balanced  by< 
saturated  earth  outside,  its  horizontal  pressure  should  also 
be  considered  as  a  force  against  the  wall. 

In  the  construction  of  these  vaults  the  forms  should 
be  kept  under  two  or  three  rows  of  vaults  beyond  any 
that  may  have  the  forms  removed,  in  order  to  make  sure« 
that  the  thrust  will  be  taken  and  the  columns  relieved  from 
taking  any  of  it. 


413 


V               A 

£ 

i  r^ 

V 

DD 

(L 

£ 

no 

i 

iJDDJ; 

pn:i 

bnji 

;i       |; 

* 

iQD;! 

^ 

^    , 

ij     I* 

. 

0) 

|DD; 

K 

ji         '! 

1 

o> 

!DD:J 
i,  -/ 

1 

Z 
^ 

414 


Base  of  Pat/ 


High  Wafer 


---------  P80-  ------  ->j 


"* 


"  1 

1          vAs"*  /.'i'.'^  Concr^^e 

, 

'"£*> 

-6"           e"> 

r  m  r  nxr  rr  n^gy  '  "  ^  "^ 

f* 

1 

2  Layers,  ^.'diam  Rods 
iZ'cenfers 

1 

1 

/cw  /ttr/*/- 

J:3:&  Concrete 

$«•' 

^ 

j£A*   x&j 

"Ta       /:%:(!>         (^ 

_^f  

k^2 

'      T 


JO'/ong 


1  r^  ri  n  ^  r  n  n  n  n  p  r 

!  i1!       i    i 


\1 


°? 

--i 


i 

i 


Bottom  offt/es 

about  9O'3'be/ort 

Base  of  fftti/ 


Plan   and   Elevation   of   River  Piers. 
415 


:::;;::;::;;:::;:| 

0  0  0  0  0  C 

'  0  0  0  0  0  0 

416 


'."    ft     .»>    C 

lyV ;<?** J«L-j4;r^/— h^-;/J5»-— >f 


QC 


418 


419 


J 


M 


ft.. 

o" 


I 


kl 
JE 

O 

I 


LLki 


£ 

£ 


j 
I 


.r,T 


427 


429 


c 

3 


« 

*> 


O       . 

O    > 


O     v 

"v    o 


rr3=£f 

^#t-**aH 
H^H 

!*— -fofi—vszt- 

ftl>i 

ri  j;.ias>: 


& 


£* 

f  _.. 


^ 

?e 

*? 

S'^J 


'  J^T 

IP 


432 


UJ 


433 


s 

<s\ 


v: 

I 

hi 
tf 
tf 

t 
t 

I 


M 


437 


co 
cvj 


4 


>c 
I 


5 

S 


438 


439 


440 


I 


441 


443 


441 


INDEX 


Adhesion,      of     concrete     to 

steel,   127,    128,    215,    220. 
Aggregates,  39-43. 
Anchor  bolts,  350. 
Anchored  rods,   75,    192,   247. 

248. 
Anchorage,    suspension 

bridge,  341. 
Arch, 

abutments,   315,   322,    323. 

bridges,     cost     of — ,     153, 

154. 

centering,    421-429. 
Arches, 

—13-16,     298-327,     410-413, 

418-421,  441. 

design   of   reinforced   con- 
crete, 298-327. 

proportions  of — ,  314. 

standard  loading,  311. 
Arch  spans,   short,   318-321. 
Asphaltum,  cost  of — ,  158. 

Battered  abutments,   145. 
Beam,   formulas,    188,    276. 
Beams, 

and  girders,   144. 

and     slabs,     design     of — , 

182-204,  214,  216,  225,   274- 

298. 

Beam,  test,   11. 
Bearing, 

power   of   soils,    328. 

power  of  masonry,  344. 
Blocks,   concrete,    82,   83,    91, 

138 

Box  culverts,   143,  432. 
Brick, 

cost  of — ,   158. 

stack,  cost  of — ,  157. 
Bridges,  cost  per  unit,  152, 

155. 

Briquette,    form  of — ,    178. 
Broken  stone,  40. 

weight  of — ,  42. 

Bronze,  cost  of — ,  158. 
Buildings,      cost     per     unit, 

153,   154. 
Cast  iron, 

columns,   146,  373. 

cost  of — ,  158. 
Cast  members,  83. 
Cement,   20-33. 

cost  of — .  159. 

natural,  20,  170. 

nature  of — ,  26-33. 

Portland,   20,   171. 


Puzzolan,   21,    26. 

Slag,   20. 

specific     gravity,      23,      24, 

173,    174. 

specifications,   168-181. 

soundness,   22,  25,   180. 

weight  of — ,   22. 
Cement  skin,  to  remove,   99- 

101. 

Cement  tests,   47,   49,   50. 
Chicago      foundations,       334, 

335. 
Chimneys,    design   of — ,   392- 

400. 
Cinder,     concrete,      78,      141, 

191. 

Cinders,    43. 
Cisterns,  144. 
Clay,  cost  of — ,  159. 
Coefficient  of  expansion, 

128. 

Coloring  surraces,  101. 
Columns   and   wall    footings, 

209-211,    216. 
Columns,   design   of,     6,    211- 

214,  230-238,   273,  370-381. 
Column, 

formulas,     213,      214,      379, 

380. 

test,  5. 
Compression   on  concrete,   6, 

119-123. 
Concrete,  57-69. 

cost    of     159. 

consistency  of,   61-66,   260, 

261. 

compressive   strength,  119- 

124. 

mixing,    54,    55,   56,    60,    61. 

tensile  strength,   124. 

weight  of — ,   141. 

blocks,   82,   83,   91,   138. 

cubes,  tests  on — ,  119-123, 

in     freezing     weather,    f~ 

89. 

in     high     temperature,    ! 

130. 

in  place,  86. 

in  polluted  water,  8b. 

pavements,      86,      87,     103, 

104. 

piles,  84,  333,  334. 

—steel    beams   and     slabs, 

182-214. 

under    water,    84,    85,    90,' 

338 
Conical   coverings,     etc.,    de- 


445 


sign  of — ,    401-413. 
Constancy  of  volume,   180. 
Continuous   beams,   280-282. 
Continuous     rods,     262,     272, 

290. 
Contraction    and     expansion, 

142. 

Contractor's  guaranty,   259. 
Corners  of  walls,   146. 
Copper,  cost  of — ,  159. 
Corrugated   steel,   cost   of — , 

155,  156. 

Cost,    estimating,    148-167. 
Crossing,   432. 

Crusher  dust,  tests,  49,   50. 
Culverts,    143,    433-435,    437- 

440. 

Curved-up  rods,   192,   272. 
Curb, 

cost  of — ,    159. 

detail,  442. 
Dams,   17,   382-391. 
Deflection  of  beams,   125. 
Depth    of   beams,     195,     199, 

202. 

Distribution  of  steel,  266. 
Domes,  etc..  design    of — ,    401- 

413. 

Drainage,  141. 
Dredging, 

cost  of — ,   160. 

hydraulic,   337. 
'open,  338. 

Drying  of  concrete,  91. 
t>ust,  crusher^  42,  49,   50. 
tEquipment,  148. 
Estimating  cost,    148-167. 
Excavating,  336-339. 
Excavating,   cost   of — ,    160. 
Expansion     and    contraction, 

142,   262. 

Factor  of  safety,  222,  383. 
Pence, 

cost  of,  161. 

posts,    147. 

Filling,  cost  of — ,  161. 
Filter  covers,   410-413. 
Fineness  of  cement,   174. 
Finishing   Concrete    Sur- 
faces,  93-110,   146. 
Fireproofing  tests,    130. 
Fire  resistant,   129. 
Flag  stone,  cost  of — ,   161. 
Flat   plate  theories,     11,     12, 

13,    286-289. 
Flat  bars,   265. 
Floor. 

support,  146. 

Ttest,     measuring     deflec- 
tions, 256,  257. 
Footings, 

reinforced  concrete,  9,    209, 


210,      216,     224,     225,     353- 

356. 

with  steel  beams,   345-348. 
Forms, 

cost  of — ,    161. 

for    concrete     work,     110- 

118. 
Foundations,      design      of — , 

327-356 
Freezing,  effect  on  concrete, 

51,   52. 

Freight,  cost  of — ,  150. 
French  drain,  cost  of — ,  161. 
Fuel,  cost  of — ,  161. 
Galvanizing,  cost  of — ,  156. 
Gang  for  mixing,   149. 
General  notes,    141-148. 
Gravel,   39,    42,   129,    137. 

cost   of — ,   161. 

weight  of — ,  42. 
Grip    of    concrete    on    steel, 

128,  186,  264,  271. 
Grout,   56,   57. 

Handling  and    placing    con- 
crete, 76-88. 

Hauling,  cost  of — ,  151. 
Heating  ingredients,  53. 
High  steel  in  concrete,  70, 

184. 

Hire  of  plant,  151,  156. 
Holes    for   pipes    and    wires, 

145. 
Hooping, 

in  chimneys,   7. 

in   columns,    212,    213,    273, 

374-379. 
Ice  tanks,   138. 
Inspection   of  work,   69,    259. 
Insulation,      with      concrete, 

138. 

Joining  to  old  concrete,  82. 
Lead,  cost  of,  161. 
Lime,    33-35. 

cost  of — ,  161. 
Limiting, 

depth   of  beams,    190,    273, 

278. 

size  of  rods,  186,  205. 
Longitudinal     reinforcement 

in  columns,  5,  75,  212,  213, 

371-374. 
Macadam  pavement,  cost  of 

— ,  151,  163. 
Manure,   action   on  concrete. 

50. 
Masonry, 

cost  of — s  161. 

strength   of — ,  349. 
Maximum,      capacity     of 

beams,   191,  207. 
Measuring    ingredients,      67, 

68. 


446 


Mineral     wool,      cost     of — , 

162. 
Mixing, 

cement,   178. 

concrete,    54-56,   60,   61. 

cost  of — ,  149. 
Modulus     of     elasticity,    71, 

126,   127. 

Molding  cement,  179. 
Molds  for  test,    178. 
Mortar,  44-57. 

finish,    96. 

strength  of  cement— 46, 47, 49, 50 

strength  of  lime— 44. 
Natural     cement,     specifica- 
tions, 170. 
Needle  beams,  355. 
Neutral   axis,     187,   198.   206, 

222,   270. 
Notes  on  general  design  and 

construction,   141-148. 
Oil,  effect  on  concrete,  51. 
Paint,  cost  of — ,  162. 
Painting,  cost  of — ,  156. 
Paper,   98. 

Partitions,      reinforced    con- 
crete, 133. 

Pavements,  86,  87,  102-106. 
Paving,  cost  of — ,  162-164. 
Percentage  of  steel,  188, 

195,   198,   200,    206. 
Permeability       of     concrete. 

134-137. 

Piers,  350-352.  414-417. 
Pile  protection,  148.  444 
Piles. 

bearing  power  of,  332,  335. 

concrete,  84.  333,  334. 

cost  of — ,   164. 

screw,  335. 

Piling,  cost  of — .   164. 
Pipe, 

concrete,   442. 

cost  of — ,  165. 
Plastering,    107,    108. 
Portland     cement    specifica- 
tions,  171. 

Practical  tests,  204,  260. 
Preservation    of    steel.     128. 

264. 
Properties   of   concrete,    118- 

141. 
Quantities, 

for  concrete,   66. 

for  mortar,  47,  48. 
Bailing, 

cost  of — ,   165. 

detail,    441,    443,    444. 
Railroads,  cost  of — per  mile. 

158. 
Reinforced  Concrete  Columns  and 

Footings,  The  Design  of—,  204- 

214,  219,  223,  224. 


Reinforced  Concrete  Engineering 

in  the  Making,  258-273. 
Retaining     walls,     17,     239- 

255. 
Retempered      concrete,       56. 

76. 

Rivets,  cost  of  driving,   156. 
Rods,    sharp    bends    in — ,   9, 

75,   248,   266,   267. 
Roofing,  cost  of — ,   156,   165.! 
Sand,  35-38. 

blasting,   cost  of — ,    165. 

cost  of — ,   165. 
Salt  in  concrete,  52. 
Sampling  cement,  173. 
Sawdust  in  concrete,   108. 
Seawater,  concrete  in—-,  139, 

140. 

Seeding,  cost  of — ,  165. 
Segmental  floor  arches,   266. 
Setting     and     hardening     of 

concrete,  88-93. 
Sewer  pipe,  cost  of,  165. 
Shaft  hangers,  145. 
Sharp   bends   in   rods,    9,    75 

248,  266,   267. 
Shear  failures,  205,  215,  221, 

363,   364. 
Shear   in  concrete,    126,    189 

356-370. 
Shearing  tests,   357-360,   367 
Shear  in  steel,   7,   268,  366. 
Shrinkage    of    concrete,     14 

185,    228,    229. 
Shrubs,  cost  of — .    165. 
Slag,  43. 

cement,   25,   26. 
Slender   columns,    146,    380. 
Sodding,  cost  of — .  165. 
Specifications      for     cement 

168-181. 
Specific     gravity   of   cement 

23,   24,  173,   174. 
Stair  supports,    144. 
Standard   concrete,    183,   261 : 
Standard  sand,    177. 
Steel   columns     in     concrete 

146,   381. 
Steel, 

cost  of — ,   165. 

for      reinforced     concrete 

70-76. 

stack,  cost  of — ,  156. 
Stirrups,  190.  215,  366. 
Stone, 

broken,  weight  of — ,  42. 

cost  of — ,   166. 

facings,  94,   95. 
Storage  of  tests,    179. 
Sulphur  in  pipe   cement,   27 

28. 
Surface, 

cracks,  90. 


447 


finish,  93-110,  146. 
Survey  of  concrete  field.   4- 

19. 

Tanks,  143,  405,  409. 
Tar,  cost  of — ,  166. 
Tarred  paper,  cost  of — ,  166. 
T-beams,     8,     207,     218,     223. 

265,    291-298. 
Tensile, 

strength   of   cement,    180. 

value     of     concrete,     186, 

367,   369. 
Tests,      interpretation     of — . 

18. 

Ties,  cost  of — ,   166. 
Tile  in  construction,   133. 
Time, 

of  setting,  176. 

to   remove  forms,   92,   263. 
Tooling,    cost   of — ,    166. 
Transverse  strength  of  con- 
crete,  126. 

Transporting,  cost  of — ,  166. 
Trap  rock,  40,  129,  138. 
Treating     wood,    cost     of — , 

166. 

Trees,  cost  of — ,  166. 
Trestle, 

ballasted,   cost   of — ,   157. 

reinforced  concrete,  8. 

steel,  cost  of — ,  157. 


timber,  cost  of — ,  157. 
Tunnels,    430,   431,    436. 
Unit    compression,     6,  7,  124, 

125,     183,      213,     275,      301, 

316,     349,      374,     378,      380, 

399. 
Unit  tension  in  steel,  18,  70, 

184,      186,     187,      209,     245, 

268,     275,      355,     37&,      398. 
Unity   in   steel,    10,    262. 
Uses  of  concrete,  147. 
Vaults,     etc.,     design     of — , 

401-413. 

Vertical  pipes,  145. 
Viaduct  bents  in  concrete,  8. 
Voids,   measuring,   59. 
Water, 

for  cement,  176. 

for   concrete,    54,    66,    89. 

for  mortar,  49. 
Waterproof, 

concrete,    134-137. 

plaster,   147. 
Whitewash,  148. 
Wire  cables  in  concrete,  74. 
Wood, 

beams  and  posts  of — ,  114. 

cost  of — ,  167. 

comparison  with  concrete, 

5,  7. 


448 


Expedition  for  Contractors 

9111 

in  the  completion  of  important  work,  is  made 
possible  by  the  promptness  with  which  we 
can  ship  from  our  big  new  warehouse 

I      Everything  Needful 
I   in  Contractors' Equipment 

Particularly : 

Ransome  Concrete  Mixing  and  Handling 
Machinery  ;  Twisted  Steel  Bars  for  Re- 
inforced Concrete  Construction  ;  Hoisting 
Engines;  Conveying  Machinery  ;  Clam  Shell 
or  Orange  Peel  Buckets ;  Hydraulic  and 
Dredging  Pumps ;  Locomotive  Cranes ; 
Steam  Shovels ;  Excavators ;  Concrete 
Hoists  and  Buckets ;  Dump  Cars ;  Steel 
Sheet  Piling ;  Troy  Wagons  ;  etc.,  etc. 

iWhat  is  YOUR  urgent  need  right  NOW  ?  Write  us 
for  prices  and  valuable  Handbook  of  Information. 
TEST  OUR  EXPEDITION. 

William  B.  Hough  Company 

MONADNOCK  BUILDING         CHICAGO,  ILL. 

i. 


The  ™ 
Railroad 
Gazette 


Contains  each  week  the  best  and  latest  infor- 
mation on  all  branches  of  Railroad  En- 
gineering—  the  best  engravings,  news 
and  discussions.  Everyone  who  desires 
to  keep  informed  on  this  branch  of  pro- 
fessional work  should  read  it. 

WEEKLY— Subscription,  $5  yearly  to 
United  States  and  Mexico;  Canada,  $6; 
Foreign,  $8.  Sample  Copy  Free. 

RAILROAD  BOOKS.  Send  for  Cata- 
logue. 

ADVERTISING  RATES  on  application. 



New  York,  83  Fulton  Street 
Chicago,  Old  Colony  Building 
London,  Queen  Anne's  Chambers 

,'  r  .o  -.  •..:, 

ii. 


AERIAL  WIRE  ROPE  TRAMWAYS 

MANUFACTURED    BY 

A.  Leschen  &  Sons  Rope  Co.,  St.  Louis,  Mo. 


Economical  transportation  of  material  such  as  Ore, 
Coal,  Stone,  Earth,  Sand,  Rock  and  Timber,  from  one 
place  to  another. 

I/>w  cost  of  operation;  small  expense  for  maintenance; 
not  affedled  by  the  elements;  free  from  surface  traffic; 
built  in  a  straight  line;  requires  no  cuts,  fills,  bridges  or 
winding  detours. 

Can  be  successfully  operated  over  distances  varying 
from  a  few  hundred  feet  to  practically  any  length  beyond. 
The  lyESCHEN  CO.'S  PATENT  AUTOMATIC  Wire 
Rope  Tramway  built  for  the  Penn-Wyoming  Copper  Co., 
Encampment,  Wyoming,  is  16  miles  long. 

This  may  vary  from  a  few  tons  to  one  hundred  tons  per 
hour,  and  in  excess  of  this  amount  in  many  cases. 

If  inclination  is  sufficient  and  the  loads  descend,  the 
tramway  will  operate  by  force  due  to  gravity,  the  sur- 
plus power  being  controlled  by  brakes.  Power,  when 
necessary,  is  applied  at  either  terminal  station. 

Double  Rope  Tramway— Single  Rope  Tramway— TWo- 
Bucket  Tramway. 

This  is  most  economical  type  both  in  cost  of  operation 
and  maintenance.  Carriers  travel  on  independent  track 
ropes,  are  propelled  and  controlled  by  endless  tradtion 
rope;  towers  support  cable  at  intervals  depending  upon 
contour  of  ground,  average  spacing  being  300  feet. 
IvESCHEN  CO.'S  PATENT  AUTOMATIC  Tramway  is 
an  automatic  type  of  the  double  rope  system  in  which 
but  one  operator  is  required. 

Endless  wire  rope  to  which  carriers  are  positively  at- 
tached; buckets  loaded  by  Mechanical  leader;  towers 
support  cable  at  intervals,  speed  about  150  feet  per  min- 
ute. Not  recommended  for  heavy  capacity  or  long 
lengths. 

Two  carriers  are  used  each  traveling  backward  and  for- 
ward on  a  track  rope.  A  light  endless  tradtion  rope 
used  for  propelling  the  carriers.  This  is  simplest  and 
least  expensive  system  when  line  is  short  and  contour 
of  ground  favorable. 

Tramway  route  should  be  surveyed  in  straight  line  con- 
necting terminal  points.  Angles  in  horizontal  plane  to 
be  avoided.  If  angle  is  absolutely  necessary  an  extra 
station  is  required  at  angle  point. 

The  A.  I.ESCHEN  &  SONS  ROPE  COMPANY  will 
furnish  estimates  of  cost  upon  receipt  of  profile  of  line 
and  definite  data  as  to  capacity  per  hour,  class  of 
material  to  be  handled,  weight  of  material  per  cubic 
foot,  and  terminal  requirements. 

An  Approximate  Estimate  can  be  given,  if  profile  is  not 
procurable,  upon  receipt  of  the  data  mentioned. 

Above  data  furnished  by  A.  LESCHEN  &  SONS  ROPE  CO.,  St.  Louis,  Mo. 


Adaptation. 
Advantages. 

Length. 

Capacity. 

Power 
Required  or 
Developed. 

Systems. 

Double 

Rope 

Tramway. 


Single 

Line 

Tramway. 

Two-Bucket 
Tramway. 


Selection 
of  Route. 

Cost. 


III. 


PATENT  FLATTENED  STRAND  WIRE  ROPES 


C 


A.  Leschen  &  Sons  Rope  Co.,  St.  Louis,  Mo.\ 

SOLE   MANUFACTURERS  / 


A— (5x28)  B-(6x25)  C— (5x9)  D— (6x8) 

HOISTING  ROPES  HAULAGE  ROPES 

With  the  view  of  increasing  the  wearing  surface  of  wire  rope  and  I 
thereby  prolonging  the  life  of  the  rope,  A.  I^eschen  &  Sons  Rope  Co.  have 
had  on  the  market  for  many  years  a  patent  flattened  strand  wire  rope  of  I 
which  they  are  sole  makers.    The  illustrations  given  above  show  in  cross  I 
sections  the  construction  of  this  style  of  rope.     These  flattened  strand  I 
wire  ropes  are  made  in  various  grades  of  material.    The  satisfaction  these 
wire  ropes  have  given  justifies  the  manufacturers*  claim  for  superiority 
over  any  wire  rope  manufactured.    The  accompanying  illustrations  show 
the  comparative  wearing  surface  between  patent  flattened  strand  and  the 
round  or  ordinary  construction  of  wire  rope. 


PATENT  FLATTENED  STRAND  ROUND  STRAND 

We  give  herewith  Table  of  Weights,  Breaking  Strains,  I^ist  Prices, 
etc.,  commencing  with  the  highest  grade  : 

"HERCULES"  PATENT   FLATTENED   STRAND. 


HOISTING                                                        HAULAGE 

en 

en 

o 

<L)        0 

a      p 

Diameter  in 
Inches 

*Priceperfo 
in  cents 

Approximat 
breaking 
strain  in  toi 
of  2,000  Ibs. 

Average 
weight  per  1 

Diameter  in 
Inches 

Price  per  foe 
in  cents 

rt      5S* 

1  ^.55 
§3j| 

|21« 

§^   MO 

Average 
weight  peri 

% 

20% 

13% 

.44 

H 

16% 

13 

.44 

X8 

28 

22% 

.73 

H 

25 

21 

.73 

x£ 

37V 

.  32 

1.00 

?4 

35 

80 

1.00    I 

YQ 

49 

40>£ 

1.35 

% 

44 

38 

1.35    1 

1 

60 

56 

1.80 

1 

58 

53 

1.80 

1% 

71 

67 

2.30 

1/i? 

70 

64 

2.30 

1/4 

89 

84 

2.80 

1/4 

88 

80 

2.80 

J1Z 

137 

124 

4.00 

1% 

208 

168 

5.40 

2 

225 

211 

7.50 

2^4 

285 

260 

9.25 

*  The  purpose  of  giving  these  list  prices  is  to  give  an  idea  of  comparative 
value. 

IV. 


A.   LESCHEN  &  SONS  ROPE  CO. 

SOLE   MANUFACTURERS 

PATENT  FLATTENED  STRAND  WIRE  ROPES 

CRUCIBLE  CAST  STEEL 
1                    HOISTING  ROPE 

SPECIAL  STEEL 
HOISTING  ROPE 

Diameter  in 
Inches 

I 

if 
I-5 

-1  JN 
•|  3  .g  § 

§££"3 

1 
•5  ^ 

•a  ®'a 

111 

3*a 

.3 

jl 

S*"4 

|| 

!•* 

Ijf-sJ 

PB** 
&ai 

1 

!l 

u 

S^« 

1i-a 
III 

1*5 
pi 

|4 

i/8 

1 
i?l 

iH 

r 

2M 

14>2 
18fc 
24 
30 

8* 

S8* 

86 
96 
121 
144 
182 

f. 

21 
29 
38 
47 
56 
69 
81 
94 
109 
140 
176 

.44 
.73 

1.00 
1.35 
1.80 
2.30 
2.80 
3.40 
4.00 
4.75 
5.40 
7.50 
9.25 

ty> 

3 

3^ 

^ 

i 

6^ 

F 

9 

17/* 
1^ 
IK 
1^ 

$ 

$K 

17% 
19K 
22>| 
30 
38 
48 
59 
70 
105 
155 
177 
220 

P 

17 

24^ 
33 
43 
54 
64 
93 
127 
162 
204 

.44 
.54 
.73 
1.00 
1.35 
1.80 
2.30 
2.80 
4.00 
5.40 
7.50 
9.25 

1K 
1% 

2 
3 

3K 

fe 

5^ 

P 

9 

HAULAGE  ROPE 

HAULAGE  ROPE 

P 
^ 

if 

7 
10 
14 
20J4 

g* 

45 

54 

5 
9 
14 
20 
27 
36 
45 
54 

.25 
.44 
.73 
1.00 
1.35 
1.80 
2.30 
2.80 

I 

1 

S 

11 
14 
18 
27 
35 
45 
54 
68 

10^ 

i* 

31 
40 
50 
62 

.25 
.44 
.73 
1.00 
1.35 
1.80 
2.30 
2.80 

2 

2^ 
3% 

4K 
5 
5% 

g3 

7^4 

These  ropes  are  made  of  the  best 
crucible  steel  wire,  combining  in  a 
high    degree   ductility  and   tensile 
strength. 

As  the  name  indicates,  this  rope 
is  made  from  a   special   grade   of 
steel,    combining    high   tensile 
strength  with  flexibility,  without  a 
tendency  to  brittleness. 

PATENT  FLATTENED  STRAND  SWEDES  IRON 

HOISTING 

HAULAGE 

I 

1 

M 

Jg 

l^Ss 

•33  a  g 

i,rjsf 

j|<aQ  33^ 

I* 

1*. 

8  ta^ 

*  °.3 

111 
l"3^ 

.a 

it 

s 

1 

M 

^    I.M 

g  be  e3  —  ' 

pi? 

1 

h 
P 

is- 

111 

"T/ 
1/8 

\Y8 

i$l 
"  i% 

2 

.     2K 

15>| 
21 
26 
34 
43 
52 

& 

82 
104 
120 

152 

4 
6 
9 
13 
17 
21 
28 
34 
40 
45 
54 
66 
75 

.38 
.57 
.83 
1.20 
1.58 
2.00 
2.50 
3.00 
3.65 
4.15 
5.00 
6.30 
8.00 

2 
3 

P 

4% 
5M 

P 

Jfvl 

1 

1% 
H? 

8H 
12)1 
17/l 
22 
29 

IK 

5? 

/ 
10 

f 

p^ 

.38 
.60 

•£7 

1.^0 
1.58 
2.00 
2.50 

ay, 
$, 

6 
6% 
J& 

8^| 
9K 

V. 


GALVANIZED 
IRON 

WIRE    ROPE 


7  WIRES        FOR    SHIPS'    RIGGING,    GUYS        12  WIRES 
FOR   DERRICKS,   ETC. 


6  STRANDS.  7  WIRES 

a 

£ 

a 

~          t4H 

i 

fl 

+j 

g 

«« 

^ 

£& 

2 

.»     v- 
w     ^ 

i 

8  1  8-1 

c  fl  o  r 

JAZ* 

£3 

i 

'S     fc 

K          fi 

o 

n  C  o  ri 

.2^ 

pproxima 
diameter 
inches 

rcumfere 
inches 

PI 
I  si 

i| 

ircumfere 
inches  of 
Manila  R 
equal  stre 

.c  o 

11 

pproxima 
diameter 
inches 

ircumfere 
inches 

stimated  ^ 
per  foot 
Hemp  cei 

rice  per  fo 
cents 

ircumfere 
inches  of 
Manila  R 
equal  stre 

fl 

< 

0 

H 

s 

U 

n 

2 

U 

W 

M 

U 

pq 

2 

6 

6.00 

12 

50 

i 

3 

1.44 

14 

54 

13. 

If 

5J 

4.85 

44 

11 

44 

i 

2f 

1.21 

12 

to 

11. 

itt 

5J 

4.40 

41 

10i 

40 

it 

21 

1.00 

10 

5 

9. 

1.1 

5 

4.00 

38 

10 

36 

i 

2J 

0.81 

9 

4| 

7  «" 

1} 

4f 

3.60 

35 

9J 

32 

i 

2 

0.64 

8 

4i 

5.^ 

*A 

41 

3.25 

31 

9 

29 

A 

If 

0.49 

7 

3| 

4.-^ 

if 

4J 

2.90 

27 

8| 

26 

i 

1} 

0.36 

6 

3 

3.1 

U 

4 

2.55 

24 

8 

23 

TO 

1} 

0.25 

5 

2j 

2.£ 

Hi 

3i 

2.25 

21 

7} 

20 

1 

H 

0.20 

4 

2f 

W 

U 

3J 

1.95 

18 

6J 

18 

A 

i 

0.16 

31 

2 

1.4 

1A 

3} 

1.70 

16 

6 

15 

5  STRANDS,  7  WIRES 

T9y 

i 

0.123 

3 

If 

1.1 

^ 

1 

0.063 

2J 

U 

0.5( 

i 

i 

0.090 

2} 

11 

0.81 

T\ 

i 

0.040 

2 

If 

0.3< 

6   STRANDS,  12  WIRES 

2 

6  ' 

6.00 

12 

50 

i! 

4} 

2.90 

29 

8} 

26 

If 

51 

4.85 

46 

11 

44 

n 

4 

2.55 

25 

8 

23 

m 

51 

4.40 

43 

10J 

40 

iT3g- 

3| 

2.25 

22 

8 

20 

5 

4.00 

40 

10 

36 

a 

31 

1.95 

19 

6J 

18 

u 

4J 

3.60 

37 

9J 

32 

1A 

31 

1.70 

17 

6 

15 

1A 

4} 

3.25 

33 

9 

29 

i 

3 

1.44 

15 

5| 

13 

VI. 


TABLE  SHOWING  BREAKING  STRAINS,  WEIGHTS, 
'RICES,  ETC.,  OF  ROUND  STRAND  WIRE  ROPES 

FOR 

HOISTING  AND  HAULAGE 

MANUFACTURED    BY 

A.    LESCHEN    &   SONS    ROPE   CO.,    ST.    LOUIS,    Mo. 


HOISTING  ROPE—  6  Strands,  19  Wires 

1 

c 

u 

a 

Breaking  Strain 
Tons  of  2,000  Ibs. 

Minimum  size 
of 
Drum  in  Feet 

lyist  Prices  per  Foot 
in  Cents 

Inches 

be 

.5 

"L 

1 

g 

1 

3 

1 

a 
o 

a 

u, 

£ 

4J 

CO 

V 

ft 

8 

cr> 

t) 

* 

« 

2 

JW 

M 

s 

1 

g 

8 

1 

s 

3 

be 
o 

1 

1 

8 

8 

'u 

51 

1 

1 

£ 

1 

4» 

3 

a 

3 
1 

1 

JD 

| 

a 

rt 

3 

«! 

W 

CO 

u 

s 

to     S 

'X 

^ 

£ 

'X 

w 

to 

0 

R 

to 

3 

2% 

9.85 

266 

222 

190 

254 

95 

13* 

9K 

9%13i 

15 

262 

210 

175 

250 

140 

2% 

2% 

8. 

238 

182 

156 

208 

78 

12 

8% 

8% 

12 

13 

229 

170 

142 

200 

117 

2% 

2 

6.30 

191 

144 

124 

165 

62 

11 

D|    8 

11 

12 

181 

134 

111 

156 

92 

2 

\$/ 

4.85 

157 

112 

96 

128 

48 

7^ 

9 

10 

166 

115 

93 

135 

80 

1% 

l->8 

4.15 

128 

97 

84 

111 

42 

oi/ 

°/2 

6^4 

6^ 

8% 

8^ 

125 

91 

74 

108 

63 

iy& 

IV 

3.55 

113 

84 

72 

96 

36 

Y--  4 

5% 

8 

7% 

109 

80 

66 

93 

57 

1% 

1% 

3. 

96 

72 

62 

82 

31 

5K 

5y 

7% 

7 

90 

67 

56 

77 

48 

l$i 

p/ 

2.45 

76 

58 

50 

67 

25 

IT; 

7 

6% 

i£ 

55 

46 

68 

40 

4 

% 

2. 

60 

49 

42 

56 

21 

•1% 

4% 

6 

6 

57% 

45 

38 

52 

33 

1% 

I 

1.58 

50 

39 

34 

44 

17 

5 

4 

! 

55% 

49 

36 

30 

43 

26 

1 

% 

1.20 

36 

30 

26 

34 

13 

4% 

3K 

4%4%! 

39 

28 

23 

34 

20 

7/8 

*A 

.89 

29 

22 

25 

tt 

! 

... 

^ 

J    4, 

30 

22 

18 

26 

16 

% 

y% 

.62 

2015& 

i»A 

186^3% 

^ 

•2% 

3%  3% 

22% 

16% 

14 

19 

12 

y& 

I9c 

.50 

1H2A 

11 

1 

14%5%|     3 

1>4 

4 

32^: 

20 

14 

12 

16 

10 

A 

!| 

% 

.39 

12  Y°A 

8T80 

11A4A,2% 

^ 

1%254 

2%i     16% 

12% 

11 

14 

08 

% 

I75 

.30 

10  7T% 

6T% 

8.853T% 

2% 

^4 

1^2% 

2 

15 

11% 

10 

13 

07% 

ire 

3/8 

.22 

75fl{, 

5 

6.552^ 

^ 

1 

i 

2 

14% 

11 

09% 

12% 

07 

% 

A 

.15 
.10 



^ 

SA 

2A 

IS 

g 

% 

7al% 
%j     1 

1 



!^ 

09% 
09 

12 

06% 
06% 

fk 

J  "HERCULES"  made  from 
which  is  made  exclusively  for  A. 

a  specially  drawn  and  patented    steel, 
I^eschen  &  Sons  Rope  Co.,  Sole  Makers. 

VII. 


TABLE— CONTINUED 

SHOWING  BREAKING  STRAINS,  WEIGHTS,  PRICES, 
ETC.,  OF  ROUND  STRAND  WIRE  ROPES 

FOR 

HOISTING    AND    HAULAGE 

MANUFACTURED    BY 
A.    LESCHEN    6.   SONS    ROPE   CO.,   ST.    LOUIS,    Mo. 


HAULAGE  ROPE—  6  Strands,  7  Wires 

1 

& 

,c 

Breaking  Strain 
in 
Tons  of  2,000  Ibs. 

Minimum  size 
of 
Drum  in  Feet 

tr. 

lyist  Prices  per        *i 
Foot  in  Cents          o 

bo 

£ 

i 

"53 

-M 

§ 

1 

2 

1 

a 

.S 

h 

si 

1 

2 

3 

& 

8 

1 

'T. 

3 

•A 

M 

S 

to 

CO 

JU 

3 

- 

S     3 

i 

|rv 

ft 
C 

1 

"o 

B 

M 

| 

1 

1 

1 

2 

3 
0 

"8 

1 

1 

bo 

'O 

1; 

Q 

< 

w 

Cfi 

0 

? 

CO 

K 

cc* 

g 

S 

CO 

w 

co 

o 

fe 

co  i  G] 

1% 

3.55 

79 

68. 

91. 

34. 

10 

S% 

8% 

10 

13 



75 

60 

90 

51 

1  51 

1* 

3. 

68 

58. 

78. 

29. 

8 

8 

9% 

12 



64 

51 

75 

43 

1^ 

1% 

2.45 

74 

56 

48. 

64. 

24. 

wMt 

'/4 

9^ 

LO/^ 

70% 

53 

43 

61 

36 

li. 

1% 

2. 

58 

46 

40. 

53. 

20. 

s  te* 

*7^ 

8 

9% 

56 

44 

36 

51 

29 

U 

1 

1.58 

47 

87 

32. 

42. 

16. 

*M 

5% 

6% 

8% 

46 

34 

28 

41 

23 

1 

% 

1.20 

33% 

28 

24. 

32. 

12. 

6 

5 

5 

6 

7% 

35 

26 

22 

32 

17% 

? 

fc 

.89 

25% 

21 

186 

24. 

9.3 

5^ 

4% 

4% 

5J4 

6% 

28 

20 

16 

25 

14 

d 

H 

.75 



18.4 

15.8 

21. 

7.9 

i 

4 

4 

5 

6 

17 

13% 

20 

12 

i! 

% 

.62 

18% 

15.1 

13.2 

17. 

6.6 

4% 

o% 

3% 

4% 

20 

14 

11 

17 

10 

^; 

A 

.50 



12.3 

10.6 

14. 

5.3 

4 

3 

3 

4 

4% 

UK 

9 

14 

8 

^ 

% 

.39 

11% 

9.70 

8.4 

11. 

4.2 

3% 

2^ 

2% 

3% 

4 

13 

9%  7K 

11 

6% 

i  , 

i  1  i 

1 

7 

.30 

7.50 

6.6 

8.55 

3.3 

3%2^ 

334 

7/4'  6%  8 

5%    T' 

Ys 

.22 

5.58 

4.8 

6.35 

2.4 

3%l2 

kC 

2*J  

6 

5%'  6% 

4H 

3 

ft 

.15 

3.88 

3.4 

4.35 

1.7 

3     1% 

15ffl3 

2%  

5% 

4%  6 

3/4 

A 

.125 

3.22 

2.8 

3.65 

1.4 

2J  

5 

*  Ux 

* 

j 

| 

I      1 

1  "HERCULES"  made  from  a  specially  drawn  and  patented  steel, 
which  is  made  exclusively  for  A.  I^eschen  &  Sons  Rope  Co.,  Sole  Makers. 

VIII. 


JNO.    J.    CONE 

A.    W.    FIERO 


ROBERT   W.    HUNT  JAS.    C.    HALLSTEt 

D.  w.   MCNAUGHER 


ROBERT  W.  HUNT  4  CO, 

ENGINEERS 

BUREAU  OF  INSPECTION,  TESTS 
AND  CONSULTATION 


Thoroughly    equipped    Chemical   and    Physical 
Laboratories  maintained  at 

Chicago,  New  York,  San  Francisco  4  London 

Inspection  and  tests  of  Rails  and  Fastenings 
Locomotives,  Cars,  Pipe,  Bridges,  Buildings 
Machinery  and  2nd  hand  equipment. 

Examination  and  reports  on  existing  structures. 
Reviews  of  metal  and  concrete-steel  construction! 

CHICAGO  :   1121  The  Rookery 

NEW  YORK:  PITTSBURG  : 

90  West  Street  Monongaheia  Bank  Building 

LONDON  :  Norfolk  House,  Cannon  Street,  £.  C. 

MONTREAL:  SAN  FRANCISCO  : 

Board  of  Trade  Building  425  Washington  Street 


X. 


Godfrey's  Tables 

[Structural  Engineering,  Book  One] 

This  book  is  a  compilation  of  tables  and  data  for 
use  in  structural  designing.  About  one-third  of  it  is 
collected  from  manufacturer's  hand-books  and  includes 
such  data  as  the  properties  of  rolled  sections,  standards 
for  bolts  and  rivets,  eyebar  tables,  fractions  to  decimals, 
and  other  tables  common  to  many  books  and  indespen- 
sable  to  the  designer.  Besides  the  foregoing  there  is 
more  new  matter  in  the  book  than  in  any  other  simi- 
lar book  published.  There  is  scarcely  a  problem  in  struc- 
tural designing  or  detailing  in  which  this  book  will  not 
be  found  useful. 

The  book  contains  more  than  200  pages.  Following 
is  a  list  of  the  contents:  Decimals  of  a  foot  and  inch. 
Properties  and  useful  dimensions  of  beams,  channels, 
angles,  zees,  tees,  rails.  Information  on  eyebars, 
clevises,  sleevenuts,  separators,  nuts,  rivets,  bolts,  cir- 
cular and  rectangular  plates,  corrugated  and  buckled 
plates.  Standard  beam  connections.  Bending  moments 
on  beams  for  concentrated  and  uniform  loads.  Deflec- 
tion formulas  in  terms  of  fibre  stress,  new.  Working 
unit  stresses  on  columns.  Ultimate  strength  of  tank 
plates,  new.  Weights  of  substances.  Conversion  table 
for  French  units.  Moments  of  inertia  of  rectangles 
varying  by  eights,  new.  Weights  and  areas  of  rods, 
bars,  and  plates.  Mensuration,  lengths  of  curves  and 
areas  if  segments,  new.  Miscellaneous  formulas  in 
usable  shape  (brake  bands,  hoops,  cylinders,  springs, 
flat  plates,  R.  R.  curves,  etc.)  Skewdetails,  hip  and  val- 
ley details,  no  angles  used,  new.  Stresses  in  eight 
styles  of  roof  trusses,  four  pitches  each.  Moments, 
shears,  etc.,  Cooper  E  50  loading  Tables  of  built  girders, 
new.  Over  2000  built  sections  with  their  properties. 
Functions  of  angles.  Typical  details,  38  pages.  Tables 
of  roots  and  circular  areas.  Tables  of  squares  of  num- 
bers to  2736.  Tables  of  squares  of  feet,  inches,  and 
fractions  for  finding  hypothenuse,  lengths  to  57  feet, 
new.  Gears,  chain,  rope.  Electric  cranes,  clearances, 
loads,  etc. 

All  of  this  in  a  small  pocktbook.  Could  anything  be 
more  useful  to  a  structural  designer,  draftsman  or  stu- 
dent? 

Book  published  by  the  Author 

EDWARD  GODFREY 

flonongahela  Bank  Building  Pittsburg,  Pa. 

Price  $2.50;   to  clubs  of  5,   $2.00. 
XI. 


Correspondence  Course 

ON 

CONCRETE 

Including  REINFORCED   CONCRETE   DESIGN,   REIN- 
FORCED CONCRETE   CONSTRUCTION,  THE 
MANUFACTURE    OF    CEMENT 
PRODUCTS. 

PARTICULARS  ON  REQUEST. 


The  following  publications  are  issued  by  our  Company 
CONCRETE  ENGINEERING,  monthly,  $1  per  year. 

CONCRETE  ENGINEERS'  &  CONTRACTORS'  POCKET- 
BOOK,  $1,  leather  binding. 

CONCRETE  CONSTRUCTION,  including  Form  work, 
Estimating,  Superintendence,  Inspection,  Cost, 
Etc.  Cloth  $1. 

THE  TECHNICAL  PUBLISHING  CO., 
Caxton  Building,      .<*--     •       Cleveland,  Ohio. 

XII. 

I!      .?"«-     ,1 


w 

C 
rt 

i 

X 

h 

0) 

^2 

H 

u 

2 

I 

S 

§s 

H 

IS* 

S 

^      1 

H     o  _S 

I 

§.« 
11 

W 

1 

^  -2    S 
^     >    co 

1* 

^ 

a 

N 

1 

2      •    w 

^         4^        G\ 

*•  g  S 

% 

ra 

I 

Q| 

< 

*c5 

c 

Q 

•S  "  « 

a    S   a 

ft      0.  >Q 

1 

U 

O 

|8| 

U 

S 

o 

*M 

CO 

0 

?S     ^ 

E 

2g 

ea 

^2 

,    V    *c5 

1-S  « 

•o    ! 
a  iT! 
«  ^ 

i 

a 

^^  s 

*£  Zt 

*-"      j        »£3 
03     ^      *"* 

o 

3  I 

1 

^^^V^    S3 

u  "~ 

^         K           QJ 

C/) 

5  u 

o  '3 

®l 
«i 

-C    C 

•S0'^ 

tl 

CD 
OS 

Q    *r*      cs 

1  I  1 

*^  1 

o     S    -2 

i 

a 
g 

i! 

!<8 

CHICAG 
Id  Colony  Bi 

IMM 

T3 

7:2   *53o    S 

8 

ij 

C 

•^^^^j 

U 

*^       *J      «-rt 

K 

h 

PH      | 

*5 

S   JG     ^ 

^ 

8 

M 

M 

0 
U 

s 
S 

•*-'*-'      ^2 
u     o 

S      Q,    -G 

&  s,  > 

o-    «     S 

U     *^""*       CU 

5 

a 
o 

J, 

w 

JG  H     5 

*C 

wl 

f^^ 

h        S1 

M 

P*^ 

S 

40 

•§ 

s? 

S3 

Q 

h 

1 

H! 

H 

O 

1 

*S 

X) 

XIII. 


The  Engineering  Record 


Published  Weekly,  $3.00  a  Year. 


THE  MOST  PROGRESSIVE  JOURNAL 
OF  THE  WORLD  DEVOTED  TO 
CIVIL  ENGINEERING  AND  ALLIED 
SUBJECTS. 


For  over  twenty  years  THE  ENGINEERING 
RECORD  has  teen  the  only  publication  to  cover 
structural  engineering  adequately  and  thoroughly. 

It  publishes  a  larger  amount  of  valuahle  matter  on 
reinforced  concrete  construction  than  is  contained  in 
any  other  engineering  journal,  describing  all  work  oi 
interest  in  this  new  field,  hut  counselling  care  and  con- 
servatism in  design  and  construction. 

For  the  ENGINEER  WHO  DESIGNS,  for  the  ENGINEER 
WHO  SUPERVISES  and  for  THE  ENGINEER  AND  CONTRACTOR 
WHO  CONSTRUCTS,  THE  ENGINEERING  RECORD  is  invaluable 

A  feature  of  special  value  is  its  unrivalled  con- 
tracting news  service.  Each  issue  contains  an 
average  of  over  500  news  items  in  regard  to  new  and 
proposed  government,  municipal  and  private  engin- 
eering and  building  undertakings  in  all  parts  of  the 
country. 


SAMPLE  COPY  ON  REQUEST 

THE  ENGINEERING  RECORD 

239  W.  39th  St.  New  York,  N.  Y. 

XIV. 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW 


AN    INITIAL    FINE    OF     25     CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
THIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $1.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


25  1932 
9   1933 


LD  21-50m-8,-32 


Y A,  Of 490 


214516 


